Linear Regression Final Project

df <- as_tibble(read.table("winequality-red.csv", sep=";", header = TRUE))
df_white <- as_tibble(read.table("winequality-white.csv", sep=";", header = TRUE))

index = sample(1:nrow(df), 0.7*nrow(df)) 

train = df[index,] # Create the training data 
test = df[-index,] # Create the test data

dim(train)

## [1] 1119   12

dim(test)

## [1] 480  12

Rudimentary LM on whole dataset

lm_basic <- lm(data = df, quality ~ .)

summary(lm_basic)

## 
## Call:
## lm(formula = quality ~ ., data = df)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.68911 -0.36652 -0.04699  0.45202  2.02498 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)           2.197e+01  2.119e+01   1.036   0.3002    
## fixed.acidity         2.499e-02  2.595e-02   0.963   0.3357    
## volatile.acidity     -1.084e+00  1.211e-01  -8.948  < 2e-16 ***
## citric.acid          -1.826e-01  1.472e-01  -1.240   0.2150    
## residual.sugar        1.633e-02  1.500e-02   1.089   0.2765    
## chlorides            -1.874e+00  4.193e-01  -4.470 8.37e-06 ***
## free.sulfur.dioxide   4.361e-03  2.171e-03   2.009   0.0447 *  
## total.sulfur.dioxide -3.265e-03  7.287e-04  -4.480 8.00e-06 ***
## density              -1.788e+01  2.163e+01  -0.827   0.4086    
## pH                   -4.137e-01  1.916e-01  -2.159   0.0310 *  
## sulphates             9.163e-01  1.143e-01   8.014 2.13e-15 ***
## alcohol               2.762e-01  2.648e-02  10.429  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.648 on 1587 degrees of freedom
## Multiple R-squared:  0.3606, Adjusted R-squared:  0.3561 
## F-statistic: 81.35 on 11 and 1587 DF,  p-value: < 2.2e-16

Volatile acidity, chlorides, total sulfur dioxide, sulphates and alcohol are all very statistically significant, although our adjusted \(R^2\) is still quite low.

Ridge regression

train_control <- trainControl(method  = "cv", number = 5)

model_ridge <- train(quality ~ .,
                     data = df,
                     method = "ridge",           # method
                     trControl = train_control)        # cross validation

model_ridge

## Ridge Regression 
## 
## 1599 samples
##   11 predictor
## 
## No pre-processing
## Resampling: Cross-Validated (5 fold) 
## Summary of sample sizes: 1280, 1279, 1280, 1278, 1279 
## Resampling results across tuning parameters:
## 
##   lambda  RMSE       Rsquared   MAE      
##   0e+00   0.6528704  0.3479670  0.5060664
##   1e-04   0.6528690  0.3479702  0.5060643
##   1e-01   0.6526458  0.3490339  0.5051653
## 
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was lambda = 0.1.

#something doesn't seem to be working here

model_stepwise <- train(quality ~ .,
                        data = df,
                        method = "glmStepAIC",
                        trControl = train_control)

## Start:  AIC=2523.52
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar + 
##     chlorides + free.sulfur.dioxide + total.sulfur.dioxide + 
##     density + pH + sulphates + alcohol
## 
##                        Df Deviance    AIC
## - citric.acid           1   527.40 2521.6
## - fixed.acidity         1   527.41 2521.6
## - density               1   527.71 2522.3
## - residual.sugar        1   528.09 2523.2
## <none>                      527.38 2523.5
## - free.sulfur.dioxide   1   528.34 2523.8
## - pH                    1   528.68 2524.7
## - total.sulfur.dioxide  1   533.58 2536.5
## - chlorides             1   536.07 2542.4
## - volatile.acidity      1   549.06 2573.1
## - sulphates             1   552.36 2580.8
## - alcohol               1   560.98 2600.6
## 
## Step:  AIC=2521.55
## .outcome ~ fixed.acidity + volatile.acidity + residual.sugar + 
##     chlorides + free.sulfur.dioxide + total.sulfur.dioxide + 
##     density + pH + sulphates + alcohol
## 
##                        Df Deviance    AIC
## - fixed.acidity         1   527.42 2519.6
## - density               1   527.72 2520.3
## - residual.sugar        1   528.09 2521.2
## <none>                      527.40 2521.6
## - free.sulfur.dioxide   1   528.42 2522.0
## - pH                    1   528.69 2522.7
## - total.sulfur.dioxide  1   534.26 2536.1
## - chlorides             1   537.12 2542.9
## - sulphates             1   552.36 2578.8
## - volatile.acidity      1   557.41 2590.4
## - alcohol               1   561.23 2599.1
## 
## Step:  AIC=2519.6
## .outcome ~ volatile.acidity + residual.sugar + chlorides + free.sulfur.dioxide + 
##     total.sulfur.dioxide + density + pH + sulphates + alcohol
## 
##                        Df Deviance    AIC
## - density               1   528.10 2519.3
## - residual.sugar        1   528.16 2519.4
## <none>                      527.42 2519.6
## - free.sulfur.dioxide   1   528.46 2520.1
## - pH                    1   531.56 2527.6
## - total.sulfur.dioxide  1   534.54 2534.8
## - chlorides             1   537.52 2541.9
## - sulphates             1   552.97 2578.2
## - volatile.acidity      1   558.59 2591.1
## - alcohol               1   589.06 2659.1
## 
## Step:  AIC=2519.27
## .outcome ~ volatile.acidity + residual.sugar + chlorides + free.sulfur.dioxide + 
##     total.sulfur.dioxide + pH + sulphates + alcohol
## 
##                        Df Deviance    AIC
## - residual.sugar        1   528.39 2518.0
## <none>                      528.10 2519.3
## - free.sulfur.dioxide   1   529.27 2520.1
## - pH                    1   531.73 2526.0
## - total.sulfur.dioxide  1   534.87 2533.6
## - chlorides             1   537.90 2540.8
## - sulphates             1   553.09 2576.4
## - volatile.acidity      1   559.48 2591.2
## - alcohol               1   626.08 2735.1
## 
## Step:  AIC=2517.97
## .outcome ~ volatile.acidity + chlorides + free.sulfur.dioxide + 
##     total.sulfur.dioxide + pH + sulphates + alcohol
## 
##                        Df Deviance    AIC
## <none>                      528.39 2518.0
## - free.sulfur.dioxide   1   529.68 2519.1
## - pH                    1   532.26 2525.3
## - total.sulfur.dioxide  1   534.93 2531.7
## - chlorides             1   537.98 2539.0
## - sulphates             1   553.18 2574.6
## - volatile.acidity      1   559.67 2589.6
## - alcohol               1   628.96 2739.0
## Start:  AIC=2517.15
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar + 
##     chlorides + free.sulfur.dioxide + total.sulfur.dioxide + 
##     density + pH + sulphates + alcohol
## 
##                        Df Deviance    AIC
## - pH                    1   525.13 2516.1
## <none>                      524.76 2517.2
## - citric.acid           1   525.99 2518.1
## - free.sulfur.dioxide   1   526.19 2518.6
## - residual.sugar        1   526.21 2518.7
## - density               1   526.41 2519.2
## - fixed.acidity         1   527.15 2521.0
## - chlorides             1   531.07 2530.4
## - total.sulfur.dioxide  1   531.97 2532.6
## - sulphates             1   543.37 2559.7
## - volatile.acidity      1   550.54 2576.5
## - alcohol               1   555.68 2588.4
## 
## Step:  AIC=2516.05
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar + 
##     chlorides + free.sulfur.dioxide + total.sulfur.dioxide + 
##     density + sulphates + alcohol
## 
##                        Df Deviance    AIC
## <none>                      525.13 2516.1
## - citric.acid           1   526.31 2516.9
## - free.sulfur.dioxide   1   526.41 2517.2
## - residual.sugar        1   527.35 2519.4
## - density               1   528.98 2523.4
## - chlorides             1   531.07 2528.4
## - total.sulfur.dioxide  1   532.00 2530.7
## - fixed.acidity         1   533.12 2533.4
## - sulphates             1   544.59 2560.6
## - volatile.acidity      1   551.06 2575.7
## - alcohol               1   562.76 2602.6
## Start:  AIC=2585.23
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar + 
##     chlorides + free.sulfur.dioxide + total.sulfur.dioxide + 
##     density + pH + sulphates + alcohol
## 
##                        Df Deviance    AIC
## - fixed.acidity         1   554.30 2583.2
## - density               1   554.30 2583.2
## - residual.sugar        1   554.57 2583.9
## - citric.acid           1   555.12 2585.1
## <none>                      554.30 2585.2
## - free.sulfur.dioxide   1   555.78 2586.6
## - pH                    1   556.97 2589.4
## - total.sulfur.dioxide  1   561.07 2598.7
## - chlorides             1   562.66 2602.4
## - sulphates             1   574.27 2628.5
## - volatile.acidity      1   584.48 2651.0
## - alcohol               1   593.54 2670.7
## 
## Step:  AIC=2583.24
## .outcome ~ volatile.acidity + citric.acid + residual.sugar + 
##     chlorides + free.sulfur.dioxide + total.sulfur.dioxide + 
##     density + pH + sulphates + alcohol
## 
##                        Df Deviance    AIC
## - density               1   554.35 2581.3
## - residual.sugar        1   554.60 2581.9
## <none>                      554.30 2583.2
## - citric.acid           1   555.17 2583.2
## - free.sulfur.dioxide   1   555.82 2584.7
## - pH                    1   560.01 2594.3
## - total.sulfur.dioxide  1   561.57 2597.9
## - chlorides             1   563.24 2601.7
## - sulphates             1   574.60 2627.2
## - volatile.acidity      1   584.55 2649.1
## - alcohol               1   610.74 2705.2
## 
## Step:  AIC=2581.35
## .outcome ~ volatile.acidity + citric.acid + residual.sugar + 
##     chlorides + free.sulfur.dioxide + total.sulfur.dioxide + 
##     pH + sulphates + alcohol
## 
##                        Df Deviance    AIC
## - residual.sugar        1   554.89 2580.6
## <none>                      554.35 2581.3
## - citric.acid           1   555.24 2581.4
## - free.sulfur.dioxide   1   555.87 2582.9
## - pH                    1   560.03 2592.4
## - total.sulfur.dioxide  1   562.03 2596.9
## - chlorides             1   563.63 2600.6
## - sulphates             1   575.96 2628.2
## - volatile.acidity      1   586.38 2651.1
## - alcohol               1   647.25 2777.4
## 
## Step:  AIC=2580.59
## .outcome ~ volatile.acidity + citric.acid + chlorides + free.sulfur.dioxide + 
##     total.sulfur.dioxide + pH + sulphates + alcohol
## 
##                        Df Deviance    AIC
## - citric.acid           1   555.62 2580.3
## <none>                      554.89 2580.6
## - free.sulfur.dioxide   1   556.66 2582.7
## - pH                    1   560.64 2591.8
## - total.sulfur.dioxide  1   562.33 2595.6
## - chlorides             1   563.96 2599.3
## - sulphates             1   576.12 2626.6
## - volatile.acidity      1   586.45 2649.3
## - alcohol               1   649.49 2779.8
## 
## Step:  AIC=2580.28
## .outcome ~ volatile.acidity + chlorides + free.sulfur.dioxide + 
##     total.sulfur.dioxide + pH + sulphates + alcohol
## 
##                        Df Deviance    AIC
## <none>                      555.62 2580.3
## - free.sulfur.dioxide   1   557.71 2583.1
## - pH                    1   560.77 2590.1
## - total.sulfur.dioxide  1   563.87 2597.1
## - chlorides             1   565.72 2601.3
## - sulphates             1   576.45 2625.3
## - volatile.acidity      1   591.71 2658.7
## - alcohol               1   650.37 2779.5
## Start:  AIC=2505.48
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar + 
##     chlorides + free.sulfur.dioxide + total.sulfur.dioxide + 
##     density + pH + sulphates + alcohol
## 
##                        Df Deviance    AIC
## - residual.sugar        1   520.39 2503.5
## - density               1   520.42 2503.6
## - fixed.acidity         1   520.47 2503.7
## - citric.acid           1   520.88 2504.7
## <none>                      520.38 2505.5
## - pH                    1   522.42 2508.5
## - free.sulfur.dioxide   1   522.83 2509.5
## - chlorides             1   527.93 2521.9
## - total.sulfur.dioxide  1   529.52 2525.7
## - sulphates             1   543.79 2559.8
## - volatile.acidity      1   549.28 2572.6
## - alcohol               1   563.06 2604.3
## 
## Step:  AIC=2503.51
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + chlorides + 
##     free.sulfur.dioxide + total.sulfur.dioxide + density + pH + 
##     sulphates + alcohol
## 
##                        Df Deviance    AIC
## - density               1   520.43 2501.6
## - fixed.acidity         1   520.53 2501.8
## - citric.acid           1   520.90 2502.8
## <none>                      520.39 2503.5
## - pH                    1   522.57 2506.8
## - free.sulfur.dioxide   1   522.83 2507.5
## - chlorides             1   527.94 2519.9
## - total.sulfur.dioxide  1   529.56 2523.8
## - sulphates             1   545.02 2560.6
## - volatile.acidity      1   549.28 2570.6
## - alcohol               1   576.75 2633.0
## 
## Step:  AIC=2501.58
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + chlorides + 
##     free.sulfur.dioxide + total.sulfur.dioxide + pH + sulphates + 
##     alcohol
## 
##                        Df Deviance    AIC
## - citric.acid           1   520.92 2500.8
## - fixed.acidity         1   520.95 2500.9
## <none>                      520.43 2501.6
## - free.sulfur.dioxide   1   522.85 2505.5
## - pH                    1   522.93 2505.7
## - chlorides             1   527.94 2517.9
## - total.sulfur.dioxide  1   529.62 2522.0
## - sulphates             1   546.01 2561.0
## - volatile.acidity      1   549.50 2569.1
## - alcohol               1   615.26 2713.7
## 
## Step:  AIC=2500.8
## .outcome ~ fixed.acidity + volatile.acidity + chlorides + free.sulfur.dioxide + 
##     total.sulfur.dioxide + pH + sulphates + alcohol
## 
##                        Df Deviance    AIC
## - fixed.acidity         1   521.08 2499.2
## <none>                      520.92 2500.8
## - pH                    1   523.38 2504.8
## - free.sulfur.dioxide   1   523.76 2505.8
## - chlorides             1   530.27 2521.5
## - total.sulfur.dioxide  1   532.03 2525.8
## - sulphates             1   546.31 2559.7
## - volatile.acidity      1   555.84 2581.8
## - alcohol               1   617.53 2716.4
## 
## Step:  AIC=2499.19
## .outcome ~ volatile.acidity + chlorides + free.sulfur.dioxide + 
##     total.sulfur.dioxide + pH + sulphates + alcohol
## 
##                        Df Deviance    AIC
## <none>                      521.08 2499.2
## - free.sulfur.dioxide   1   523.88 2504.0
## - pH                    1   526.89 2511.4
## - chlorides             1   530.99 2521.3
## - total.sulfur.dioxide  1   532.72 2525.4
## - sulphates             1   546.96 2559.2
## - volatile.acidity      1   556.49 2581.3
## - alcohol               1   617.85 2715.1
## Start:  AIC=2534.99
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar + 
##     chlorides + free.sulfur.dioxide + total.sulfur.dioxide + 
##     density + pH + sulphates + alcohol
## 
##                        Df Deviance    AIC
## - residual.sugar        1   532.99 2534.1
## - fixed.acidity         1   533.07 2534.3
## - citric.acid           1   533.08 2534.3
## - density               1   533.22 2534.7
## <none>                      532.53 2535.0
## - free.sulfur.dioxide   1   533.48 2535.3
## - pH                    1   534.60 2538.0
## - chlorides             1   535.87 2541.0
## - total.sulfur.dioxide  1   537.58 2545.1
## - sulphates             1   553.65 2582.7
## - volatile.acidity      1   559.84 2597.0
## - alcohol               1   569.44 2618.7
## 
## Step:  AIC=2534.1
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + chlorides + 
##     free.sulfur.dioxide + total.sulfur.dioxide + density + pH + 
##     sulphates + alcohol
## 
##                        Df Deviance    AIC
## - fixed.acidity         1   533.24 2532.7
## - density               1   533.28 2532.8
## - citric.acid           1   533.48 2533.3
## <none>                      532.99 2534.1
## - free.sulfur.dioxide   1   534.11 2534.8
## - pH                    1   536.07 2539.5
## - chlorides             1   536.40 2540.2
## - total.sulfur.dioxide  1   537.90 2543.8
## - sulphates             1   553.70 2580.8
## - volatile.acidity      1   560.41 2596.2
## - alcohol               1   587.08 2655.7
## 
## Step:  AIC=2532.69
## .outcome ~ volatile.acidity + citric.acid + chlorides + free.sulfur.dioxide + 
##     total.sulfur.dioxide + density + pH + sulphates + alcohol
## 
##                        Df Deviance    AIC
## - density               1   533.30 2530.8
## - citric.acid           1   533.56 2531.5
## <none>                      533.24 2532.7
## - free.sulfur.dioxide   1   534.45 2533.6
## - chlorides             1   537.35 2540.5
## - total.sulfur.dioxide  1   539.40 2545.4
## - pH                    1   541.38 2550.1
## - sulphates             1   553.73 2578.9
## - volatile.acidity      1   560.44 2594.3
## - alcohol               1   600.78 2683.2
## 
## Step:  AIC=2530.84
## .outcome ~ volatile.acidity + citric.acid + chlorides + free.sulfur.dioxide + 
##     total.sulfur.dioxide + pH + sulphates + alcohol
## 
##                        Df Deviance    AIC
## - citric.acid           1   533.90 2530.3
## <none>                      533.30 2530.8
## - free.sulfur.dioxide   1   534.49 2531.7
## - chlorides             1   537.36 2538.5
## - total.sulfur.dioxide  1   539.40 2543.4
## - pH                    1   541.48 2548.3
## - sulphates             1   553.95 2577.4
## - volatile.acidity      1   563.66 2599.7
## - alcohol               1   636.04 2754.2
## 
## Step:  AIC=2530.29
## .outcome ~ volatile.acidity + chlorides + free.sulfur.dioxide + 
##     total.sulfur.dioxide + pH + sulphates + alcohol
## 
##                        Df Deviance    AIC
## <none>                      533.90 2530.3
## - free.sulfur.dioxide   1   535.35 2531.8
## - chlorides             1   538.53 2539.3
## - total.sulfur.dioxide  1   540.74 2544.6
## - pH                    1   541.96 2547.4
## - sulphates             1   554.11 2575.8
## - volatile.acidity      1   568.70 2609.0
## - alcohol               1   637.82 2755.8
## Start:  AIC=3164.28
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar + 
##     chlorides + free.sulfur.dioxide + total.sulfur.dioxide + 
##     density + pH + sulphates + alcohol
## 
##                        Df Deviance    AIC
## - density               1   666.70 3163.0
## - fixed.acidity         1   666.80 3163.2
## - residual.sugar        1   666.91 3163.5
## - citric.acid           1   667.06 3163.8
## <none>                      666.41 3164.3
## - free.sulfur.dioxide   1   668.10 3166.3
## - pH                    1   668.37 3167.0
## - chlorides             1   674.80 3182.3
## - total.sulfur.dioxide  1   674.84 3182.4
## - sulphates             1   693.38 3225.7
## - volatile.acidity      1   700.03 3241.0
## - alcohol               1   712.08 3268.3
## 
## Step:  AIC=3162.96
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar + 
##     chlorides + free.sulfur.dioxide + total.sulfur.dioxide + 
##     pH + sulphates + alcohol
## 
##                        Df Deviance    AIC
## - fixed.acidity         1   666.81 3161.2
## - residual.sugar        1   666.93 3161.5
## - citric.acid           1   667.35 3162.5
## <none>                      666.70 3163.0
## - free.sulfur.dioxide   1   668.53 3165.3
## - pH                    1   671.02 3171.3
## - total.sulfur.dioxide  1   675.43 3181.8
## - chlorides             1   675.46 3181.8
## - sulphates             1   693.98 3225.1
## - volatile.acidity      1   701.70 3242.8
## - alcohol               1   786.37 3424.9
## 
## Step:  AIC=3161.22
## .outcome ~ volatile.acidity + citric.acid + residual.sugar + 
##     chlorides + free.sulfur.dioxide + total.sulfur.dioxide + 
##     pH + sulphates + alcohol
## 
##                        Df Deviance    AIC
## - residual.sugar        1   667.06 3159.8
## - citric.acid           1   667.37 3160.6
## <none>                      666.81 3161.2
## - free.sulfur.dioxide   1   668.71 3163.8
## - pH                    1   673.87 3176.1
## - chlorides             1   676.75 3182.9
## - total.sulfur.dioxide  1   676.84 3183.1
## - sulphates             1   694.48 3224.2
## - volatile.acidity      1   703.04 3243.8
## - alcohol               1   787.44 3425.1
## 
## Step:  AIC=3159.84
## .outcome ~ volatile.acidity + citric.acid + chlorides + free.sulfur.dioxide + 
##     total.sulfur.dioxide + pH + sulphates + alcohol
## 
##                        Df Deviance    AIC
## - citric.acid           1   667.54 3159.0
## <none>                      667.06 3159.8
## - free.sulfur.dioxide   1   669.13 3162.8
## - pH                    1   674.20 3174.9
## - total.sulfur.dioxide  1   676.89 3181.2
## - chlorides             1   676.89 3181.2
## - sulphates             1   694.51 3222.3
## - volatile.acidity      1   703.04 3241.8
## - alcohol               1   789.73 3427.8
## 
## Step:  AIC=3158.98
## .outcome ~ volatile.acidity + chlorides + free.sulfur.dioxide + 
##     total.sulfur.dioxide + pH + sulphates + alcohol
## 
##                        Df Deviance    AIC
## <none>                      667.54 3159.0
## - free.sulfur.dioxide   1   669.93 3162.7
## - pH                    1   674.61 3173.8
## - total.sulfur.dioxide  1   678.32 3182.6
## - chlorides             1   678.35 3182.7
## - sulphates             1   694.60 3220.5
## - volatile.acidity      1   709.85 3255.3
## - alcohol               1   792.02 3430.4

#model_stepwise

Explore anything highly correlated:

correlation_df <- cor(df)

#correlation_df

# fixed acidity to ph and sulphates

correlation_df_melt <- melt(correlation_df)

gz <- ggplot(correlation_df_melt, mapping = aes(x = Var1, y = Var2, fill = value)) + 
  geom_tile() + 
  theme(axis.text.x = element_text(angle = 90, hjust = 1))+
  theme(text = element_text(size = 8)) + 
  ggtitle("Heat map for correlation") + 
  ylab("")+
  xlab("")+
  scale_fill_distiller(palette = "RdPu")

ggplotly(gz, tooltip = "text")

minimized_lm_df <- df %>% 
  select(-free.sulfur.dioxide, -citric.acid, -density, -volatile.acidity, -pH)

minimized_lm <- lm(data = minimized_lm_df, quality ~ .)

summary(minimized_lm)

## 
## Call:
## lm(formula = quality ~ ., data = minimized_lm_df)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.71086 -0.37485 -0.06023  0.48038  2.08242 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)           1.5204529  0.2113680   7.193 9.69e-13 ***
## fixed.acidity         0.0485196  0.0101132   4.798 1.76e-06 ***
## residual.sugar        0.0057865  0.0124562   0.465    0.642    
## chlorides            -2.3443435  0.4030377  -5.817 7.24e-09 ***
## total.sulfur.dioxide -0.0023418  0.0005467  -4.283 1.95e-05 ***
## sulphates             1.1850119  0.1116567  10.613  < 2e-16 ***
## alcohol               0.3100041  0.0171438  18.083  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6742 on 1592 degrees of freedom
## Multiple R-squared:  0.3057, Adjusted R-squared:  0.3031 
## F-statistic: 116.8 on 6 and 1592 DF,  p-value: < 2.2e-16

correlations

findCorrelation(
  cor(df),
  cutoff = 0.5,
  verbose = TRUE,
  names = TRUE
)

## Compare row 3  and column  1 with corr  0.672 
##   Means:  0.293 vs 0.19 so flagging column 3 
## Compare row 1  and column  8 with corr  0.668 
##   Means:  0.245 vs 0.172 so flagging column 1 
## Compare row 7  and column  6 with corr  0.668 
##   Means:  0.174 vs 0.169 so flagging column 7 
## All correlations <= 0.5

## [1] "citric.acid"          "fixed.acidity"        "total.sulfur.dioxide"

ggcorrplot(correlation_df, hc.order = TRUE, type = "lower")

df_less_acid <- df %>% 
  select(-citric.acid, -fixed.acidity)

lm_less_acid <- lm(data = df_less_acid, quality ~ .)
summary(lm_less_acid)

## 
## Call:
## lm(formula = quality ~ ., data = df_less_acid)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.66740 -0.37223 -0.04556  0.46264  2.03092 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          12.0575013 12.0089257   1.004   0.3155    
## volatile.acidity     -1.0127925  0.1009279 -10.035  < 2e-16 ***
## residual.sugar        0.0115046  0.0134606   0.855   0.3929    
## chlorides            -2.0490938  0.3992190  -5.133 3.21e-07 ***
## free.sulfur.dioxide   0.0048741  0.0021385   2.279   0.0228 *  
## total.sulfur.dioxide -0.0035687  0.0006939  -5.143 3.03e-07 ***
## density              -7.5668358 11.8648390  -0.638   0.5237    
## pH                   -0.4919908  0.1210931  -4.063 5.08e-05 ***
## sulphates             0.9024434  0.1129657   7.989 2.60e-15 ***
## alcohol               0.2810022  0.0201992  13.912  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.648 on 1589 degrees of freedom
## Multiple R-squared:  0.3598, Adjusted R-squared:  0.3562 
## F-statistic: 99.22 on 9 and 1589 DF,  p-value: < 2.2e-16

Lasso

plot(df)

Full scaled analysis

colnames(df)

##  [1] "fixed.acidity"        "volatile.acidity"     "citric.acid"         
##  [4] "residual.sugar"       "chlorides"            "free.sulfur.dioxide" 
##  [7] "total.sulfur.dioxide" "density"              "pH"                  
## [10] "sulphates"            "alcohol"              "quality"

cols = c('fixed.acidity', 'volatile.acidity', 'citric.acid', 'residual.sugar', 'chlorides', 'free.sulfur.dioxide', 'total.sulfur.dioxide', 'density', 'pH', 'sulphates', 'alcohol')

pre_proc_val <- preProcess(train[,cols], method = c("center", "scale"))

train[,cols] = predict(pre_proc_val, train[,cols])
test[,cols] = predict(pre_proc_val, test[,cols])

summary(train)

##  fixed.acidity     volatile.acidity    citric.acid      residual.sugar    
##  Min.   :-2.1641   Min.   :-2.33694   Min.   :-1.3873   Min.   :-1.12033  
##  1st Qu.:-0.7241   1st Qu.:-0.73547   1st Qu.:-0.8734   1st Qu.:-0.44605  
##  Median :-0.2633   Median :-0.04912   Median :-0.1026   Median :-0.24377  
##  Mean   : 0.0000   Mean   : 0.00000   Mean   : 0.0000   Mean   : 0.00000  
##  3rd Qu.: 0.5431   3rd Qu.: 0.63723   3rd Qu.: 0.7711   3rd Qu.: 0.02594  
##  Max.   : 4.1143   Max.   : 6.01361   Max.   : 2.6726   Max.   : 8.65665  
##    chlorides        free.sulfur.dioxide total.sulfur.dioxide
##  Min.   :-1.74737   Min.   :-1.4241     Min.   :-1.2284     
##  1st Qu.:-0.37937   1st Qu.:-0.7606     1st Qu.:-0.7423     
##  Median :-0.19388   Median :-0.1919     Median :-0.2561     
##  Mean   : 0.00000   Mean   : 0.0000     Mean   : 0.0000     
##  3rd Qu.: 0.08435   3rd Qu.: 0.5190     3rd Qu.: 0.4731     
##  Max.   : 8.80242   Max.   : 5.3056     Max.   : 7.3704     
##     density                pH              sulphates          alcohol       
##  Min.   :-3.541362   Min.   :-2.930364   Min.   :-2.0708   Min.   :-1.8774  
##  1st Qu.:-0.605231   1st Qu.:-0.655529   1st Qu.:-0.6664   1st Qu.:-0.8516  
##  Median :-0.006449   Median :-0.005576   Median :-0.2195   Median :-0.2920  
##  Mean   : 0.000000   Mean   : 0.000000   Mean   : 0.0000   Mean   : 0.0000  
##  3rd Qu.: 0.571322   3rd Qu.: 0.579382   3rd Qu.: 0.4827   3rd Qu.: 0.5473  
##  Max.   : 3.612502   Max.   : 4.544094   Max.   : 8.2710   Max.   : 3.3449  
##     quality     
##  Min.   :3.000  
##  1st Qu.:5.000  
##  Median :6.000  
##  Mean   :5.636  
##  3rd Qu.:6.000  
##  Max.   :8.000

#generic LM

lm_2 <- lm(quality ~ ., data = train)
summary(lm_2)

## 
## Call:
## lm(formula = quality ~ ., data = train)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.71239 -0.36588 -0.05802  0.45321  1.92777 
## 
## Coefficients:
##                      Estimate Std. Error t value Pr(>|t|)    
## (Intercept)           5.63628    0.01935 291.341  < 2e-16 ***
## fixed.acidity         0.07057    0.05421   1.302  0.19324    
## volatile.acidity     -0.16270    0.02571  -6.328 3.60e-10 ***
## citric.acid          -0.04640    0.03435  -1.351  0.17703    
## residual.sugar        0.05101    0.02553   1.998  0.04597 *  
## chlorides            -0.06809    0.02356  -2.890  0.00393 ** 
## free.sulfur.dioxide   0.05923    0.02722   2.175  0.02980 *  
## total.sulfur.dioxide -0.11349    0.02851  -3.980 7.33e-05 ***
## density              -0.08224    0.04845  -1.697  0.08992 .  
## pH                   -0.07915    0.03526  -2.245  0.02498 *  
## sulphates             0.16221    0.02295   7.067 2.79e-12 ***
## alcohol               0.27958    0.03289   8.500  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6472 on 1107 degrees of freedom
## Multiple R-squared:  0.3461, Adjusted R-squared:  0.3396 
## F-statistic: 53.26 on 11 and 1107 DF,  p-value: < 2.2e-16

Regularization

cols_reg = c('fixed.acidity', 'volatile.acidity', 'citric.acid', 'residual.sugar', 'chlorides', 'free.sulfur.dioxide', 'total.sulfur.dioxide', 'density', 'pH', 'sulphates', 'alcohol', 'quality')

dummies <- dummyVars(quality ~ ., data = df[,cols_reg])

train_dummies = predict(dummies, newdata = train[,cols_reg])

test_dummies = predict(dummies, newdata = test[,cols_reg])

print(dim(train_dummies)); print(dim(test_dummies))

## [1] 1119   11

## [1] 480  11

Ridge Regression

x = as.matrix(train_dummies)
y_train = train$quality

x_test = as.matrix(test_dummies)
y_test = test$quality

lambdas <- 10^seq(2, -3, by = -.1)
ridge_reg = glmnet(x, y_train, nlambda = 25, alpha = 0, family = 'gaussian', lambda = lambdas)

summary(ridge_reg)

##           Length Class     Mode   
## a0         51    -none-    numeric
## beta      561    dgCMatrix S4     
## df         51    -none-    numeric
## dim         2    -none-    numeric
## lambda     51    -none-    numeric
## dev.ratio  51    -none-    numeric
## nulldev     1    -none-    numeric
## npasses     1    -none-    numeric
## jerr        1    -none-    numeric
## offset      1    -none-    logical
## call        7    -none-    call   
## nobs        1    -none-    numeric

Optimal Lambda

cv_ridge <- cv.glmnet(x, y_train, alpha = 0, lambda = lambdas)
optimal_lambda <- cv_ridge$lambda.min
optimal_lambda

## [1] 0.03981072

Formal metrics for Ridge

# Compute R^2 from true and predicted values
eval_results <- function(true, predicted, df) {
  SSE <- sum((predicted - true)^2)
  SST <- sum((true - mean(true))^2)
  R_square <- 1 - SSE / SST
  RMSE = sqrt(SSE/nrow(df))

  
  # Model performance metrics
data.frame(
  RMSE = RMSE,
  Rsquare = R_square
)
  
}

# Prediction and evaluation on train data
predictions_train <- predict(ridge_reg, s = optimal_lambda, newx = x)
eval_results(y_train, predictions_train, train)

##        RMSE   Rsquare
## 1 0.6440413 0.3453163

# Prediction and evaluation on test data
predictions_test <- predict(ridge_reg, s = optimal_lambda, newx = x_test)
eval_results(y_test, predictions_test, test)

##        RMSE  Rsquare
## 1 0.6553348 0.381321

Lasso

lambdas <- 10^seq(2, -3, by = -.1)

# Setting alpha = 1 implements lasso regression
lasso_reg <- cv.glmnet(x, y_train, alpha = 1, lambda = lambdas, standardize = TRUE, nfolds = 5)

# Best 
lambda_best <- lasso_reg$lambda.min 
lambda_best

## [1] 0.001

lasso_model <- glmnet(x, y_train, alpha = 1, lambda = lambda_best, standardize = TRUE)

predictions_train <- predict(lasso_model, s = lambda_best, newx = x)
eval_results(y_train, predictions_train, train)

##        RMSE   Rsquare
## 1 0.6436934 0.3460234

predictions_test <- predict(lasso_model, s = lambda_best, newx = x_test)
eval_results(y_test, predictions_test, test)

##        RMSE   Rsquare
## 1 0.6553293 0.3813313

Mix of ridge and lasso (elasticnet)

# Set training control
train_cont <- trainControl(method = "repeatedcv",
                              number = 10,
                              repeats = 5,
                              search = "random",
                              verboseIter = TRUE)

# Train the model
elastic_reg <- train(quality ~ .,
                           data = train,
                           method = "glmnet",
                           preProcess = c("center", "scale"),
                           tuneLength = 10,
                           trControl = train_cont)

## + Fold01.Rep1: alpha=0.7034, lambda=0.215777 
## - Fold01.Rep1: alpha=0.7034, lambda=0.215777 
## + Fold01.Rep1: alpha=0.1303, lambda=2.918438 
## - Fold01.Rep1: alpha=0.1303, lambda=2.918438 
## + Fold01.Rep1: alpha=0.9303, lambda=0.013567 
## - Fold01.Rep1: alpha=0.9303, lambda=0.013567 
## + Fold01.Rep1: alpha=0.9076, lambda=3.206257 
## - Fold01.Rep1: alpha=0.9076, lambda=3.206257 
## + Fold01.Rep1: alpha=0.3536, lambda=3.736772 
## - Fold01.Rep1: alpha=0.3536, lambda=3.736772 
## + Fold01.Rep1: alpha=0.7569, lambda=0.457474 
## - Fold01.Rep1: alpha=0.7569, lambda=0.457474 
## + Fold01.Rep1: alpha=0.4423, lambda=0.004959 
## - Fold01.Rep1: alpha=0.4423, lambda=0.004959 
## + Fold01.Rep1: alpha=0.4111, lambda=0.885269 
## - Fold01.Rep1: alpha=0.4111, lambda=0.885269 
## + Fold01.Rep1: alpha=0.4419, lambda=0.014470 
## - Fold01.Rep1: alpha=0.4419, lambda=0.014470 
## + Fold01.Rep1: alpha=0.2539, lambda=6.506213 
## - Fold01.Rep1: alpha=0.2539, lambda=6.506213 
## + Fold02.Rep1: alpha=0.7034, lambda=0.215777 
## - Fold02.Rep1: alpha=0.7034, lambda=0.215777 
## + Fold02.Rep1: alpha=0.1303, lambda=2.918438 
## - Fold02.Rep1: alpha=0.1303, lambda=2.918438 
## + Fold02.Rep1: alpha=0.9303, lambda=0.013567 
## - Fold02.Rep1: alpha=0.9303, lambda=0.013567 
## + Fold02.Rep1: alpha=0.9076, lambda=3.206257 
## - Fold02.Rep1: alpha=0.9076, lambda=3.206257 
## + Fold02.Rep1: alpha=0.3536, lambda=3.736772 
## - Fold02.Rep1: alpha=0.3536, lambda=3.736772 
## + Fold02.Rep1: alpha=0.7569, lambda=0.457474 
## - Fold02.Rep1: alpha=0.7569, lambda=0.457474 
## + Fold02.Rep1: alpha=0.4423, lambda=0.004959 
## - Fold02.Rep1: alpha=0.4423, lambda=0.004959 
## + Fold02.Rep1: alpha=0.4111, lambda=0.885269 
## - Fold02.Rep1: alpha=0.4111, lambda=0.885269 
## + Fold02.Rep1: alpha=0.4419, lambda=0.014470 
## - Fold02.Rep1: alpha=0.4419, lambda=0.014470 
## + Fold02.Rep1: alpha=0.2539, lambda=6.506213 
## - Fold02.Rep1: alpha=0.2539, lambda=6.506213 
## + Fold03.Rep1: alpha=0.7034, lambda=0.215777 
## - Fold03.Rep1: alpha=0.7034, lambda=0.215777 
## + Fold03.Rep1: alpha=0.1303, lambda=2.918438 
## - Fold03.Rep1: alpha=0.1303, lambda=2.918438 
## + Fold03.Rep1: alpha=0.9303, lambda=0.013567 
## - Fold03.Rep1: alpha=0.9303, lambda=0.013567 
## + Fold03.Rep1: alpha=0.9076, lambda=3.206257 
## - Fold03.Rep1: alpha=0.9076, lambda=3.206257 
## + Fold03.Rep1: alpha=0.3536, lambda=3.736772 
## - Fold03.Rep1: alpha=0.3536, lambda=3.736772 
## + Fold03.Rep1: alpha=0.7569, lambda=0.457474 
## - Fold03.Rep1: alpha=0.7569, lambda=0.457474 
## + Fold03.Rep1: alpha=0.4423, lambda=0.004959 
## - Fold03.Rep1: alpha=0.4423, lambda=0.004959 
## + Fold03.Rep1: alpha=0.4111, lambda=0.885269 
## - Fold03.Rep1: alpha=0.4111, lambda=0.885269 
## + Fold03.Rep1: alpha=0.4419, lambda=0.014470 
## - Fold03.Rep1: alpha=0.4419, lambda=0.014470 
## + Fold03.Rep1: alpha=0.2539, lambda=6.506213 
## - Fold03.Rep1: alpha=0.2539, lambda=6.506213 
## + Fold04.Rep1: alpha=0.7034, lambda=0.215777 
## - Fold04.Rep1: alpha=0.7034, lambda=0.215777 
## + Fold04.Rep1: alpha=0.1303, lambda=2.918438 
## - Fold04.Rep1: alpha=0.1303, lambda=2.918438 
## + Fold04.Rep1: alpha=0.9303, lambda=0.013567 
## - Fold04.Rep1: alpha=0.9303, lambda=0.013567 
## + Fold04.Rep1: alpha=0.9076, lambda=3.206257 
## - Fold04.Rep1: alpha=0.9076, lambda=3.206257 
## + Fold04.Rep1: alpha=0.3536, lambda=3.736772 
## - Fold04.Rep1: alpha=0.3536, lambda=3.736772 
## + Fold04.Rep1: alpha=0.7569, lambda=0.457474 
## - Fold04.Rep1: alpha=0.7569, lambda=0.457474 
## + Fold04.Rep1: alpha=0.4423, lambda=0.004959 
## - Fold04.Rep1: alpha=0.4423, lambda=0.004959 
## + Fold04.Rep1: alpha=0.4111, lambda=0.885269 
## - Fold04.Rep1: alpha=0.4111, lambda=0.885269 
## + Fold04.Rep1: alpha=0.4419, lambda=0.014470 
## - Fold04.Rep1: alpha=0.4419, lambda=0.014470 
## + Fold04.Rep1: alpha=0.2539, lambda=6.506213 
## - Fold04.Rep1: alpha=0.2539, lambda=6.506213 
## + Fold05.Rep1: alpha=0.7034, lambda=0.215777 
## - Fold05.Rep1: alpha=0.7034, lambda=0.215777 
## + Fold05.Rep1: alpha=0.1303, lambda=2.918438 
## - Fold05.Rep1: alpha=0.1303, lambda=2.918438 
## + Fold05.Rep1: alpha=0.9303, lambda=0.013567 
## - Fold05.Rep1: alpha=0.9303, lambda=0.013567 
## + Fold05.Rep1: alpha=0.9076, lambda=3.206257 
## - Fold05.Rep1: alpha=0.9076, lambda=3.206257 
## + Fold05.Rep1: alpha=0.3536, lambda=3.736772 
## - Fold05.Rep1: alpha=0.3536, lambda=3.736772 
## + Fold05.Rep1: alpha=0.7569, lambda=0.457474 
## - Fold05.Rep1: alpha=0.7569, lambda=0.457474 
## + Fold05.Rep1: alpha=0.4423, lambda=0.004959 
## - Fold05.Rep1: alpha=0.4423, lambda=0.004959 
## + Fold05.Rep1: alpha=0.4111, lambda=0.885269 
## - Fold05.Rep1: alpha=0.4111, lambda=0.885269 
## + Fold05.Rep1: alpha=0.4419, lambda=0.014470 
## - Fold05.Rep1: alpha=0.4419, lambda=0.014470 
## + Fold05.Rep1: alpha=0.2539, lambda=6.506213 
## - Fold05.Rep1: alpha=0.2539, lambda=6.506213 
## + Fold06.Rep1: alpha=0.7034, lambda=0.215777 
## - Fold06.Rep1: alpha=0.7034, lambda=0.215777 
## + Fold06.Rep1: alpha=0.1303, lambda=2.918438 
## - Fold06.Rep1: alpha=0.1303, lambda=2.918438 
## + Fold06.Rep1: alpha=0.9303, lambda=0.013567 
## - Fold06.Rep1: alpha=0.9303, lambda=0.013567 
## + Fold06.Rep1: alpha=0.9076, lambda=3.206257 
## - Fold06.Rep1: alpha=0.9076, lambda=3.206257 
## + Fold06.Rep1: alpha=0.3536, lambda=3.736772 
## - Fold06.Rep1: alpha=0.3536, lambda=3.736772 
## + Fold06.Rep1: alpha=0.7569, lambda=0.457474 
## - Fold06.Rep1: alpha=0.7569, lambda=0.457474 
## + Fold06.Rep1: alpha=0.4423, lambda=0.004959 
## - Fold06.Rep1: alpha=0.4423, lambda=0.004959 
## + Fold06.Rep1: alpha=0.4111, lambda=0.885269 
## - Fold06.Rep1: alpha=0.4111, lambda=0.885269 
## + Fold06.Rep1: alpha=0.4419, lambda=0.014470 
## - Fold06.Rep1: alpha=0.4419, lambda=0.014470 
## + Fold06.Rep1: alpha=0.2539, lambda=6.506213 
## - Fold06.Rep1: alpha=0.2539, lambda=6.506213 
## + Fold07.Rep1: alpha=0.7034, lambda=0.215777 
## - Fold07.Rep1: alpha=0.7034, lambda=0.215777 
## + Fold07.Rep1: alpha=0.1303, lambda=2.918438 
## - Fold07.Rep1: alpha=0.1303, lambda=2.918438 
## + Fold07.Rep1: alpha=0.9303, lambda=0.013567 
## - Fold07.Rep1: alpha=0.9303, lambda=0.013567 
## + Fold07.Rep1: alpha=0.9076, lambda=3.206257 
## - Fold07.Rep1: alpha=0.9076, lambda=3.206257 
## + Fold07.Rep1: alpha=0.3536, lambda=3.736772 
## - Fold07.Rep1: alpha=0.3536, lambda=3.736772 
## + Fold07.Rep1: alpha=0.7569, lambda=0.457474 
## - Fold07.Rep1: alpha=0.7569, lambda=0.457474 
## + Fold07.Rep1: alpha=0.4423, lambda=0.004959 
## - Fold07.Rep1: alpha=0.4423, lambda=0.004959 
## + Fold07.Rep1: alpha=0.4111, lambda=0.885269 
## - Fold07.Rep1: alpha=0.4111, lambda=0.885269 
## + Fold07.Rep1: alpha=0.4419, lambda=0.014470 
## - Fold07.Rep1: alpha=0.4419, lambda=0.014470 
## + Fold07.Rep1: alpha=0.2539, lambda=6.506213 
## - Fold07.Rep1: alpha=0.2539, lambda=6.506213 
## + Fold08.Rep1: alpha=0.7034, lambda=0.215777 
## - Fold08.Rep1: alpha=0.7034, lambda=0.215777 
## + Fold08.Rep1: alpha=0.1303, lambda=2.918438 
## - Fold08.Rep1: alpha=0.1303, lambda=2.918438 
## + Fold08.Rep1: alpha=0.9303, lambda=0.013567 
## - Fold08.Rep1: alpha=0.9303, lambda=0.013567 
## + Fold08.Rep1: alpha=0.9076, lambda=3.206257 
## - Fold08.Rep1: alpha=0.9076, lambda=3.206257 
## + Fold08.Rep1: alpha=0.3536, lambda=3.736772 
## - Fold08.Rep1: alpha=0.3536, lambda=3.736772 
## + Fold08.Rep1: alpha=0.7569, lambda=0.457474 
## - Fold08.Rep1: alpha=0.7569, lambda=0.457474 
## + Fold08.Rep1: alpha=0.4423, lambda=0.004959 
## - Fold08.Rep1: alpha=0.4423, lambda=0.004959 
## + Fold08.Rep1: alpha=0.4111, lambda=0.885269 
## - Fold08.Rep1: alpha=0.4111, lambda=0.885269 
## + Fold08.Rep1: alpha=0.4419, lambda=0.014470 
## - Fold08.Rep1: alpha=0.4419, lambda=0.014470 
## + Fold08.Rep1: alpha=0.2539, lambda=6.506213 
## - Fold08.Rep1: alpha=0.2539, lambda=6.506213 
## + Fold09.Rep1: alpha=0.7034, lambda=0.215777 
## - Fold09.Rep1: alpha=0.7034, lambda=0.215777 
## + Fold09.Rep1: alpha=0.1303, lambda=2.918438 
## - Fold09.Rep1: alpha=0.1303, lambda=2.918438 
## + Fold09.Rep1: alpha=0.9303, lambda=0.013567 
## - Fold09.Rep1: alpha=0.9303, lambda=0.013567 
## + Fold09.Rep1: alpha=0.9076, lambda=3.206257 
## - Fold09.Rep1: alpha=0.9076, lambda=3.206257 
## + Fold09.Rep1: alpha=0.3536, lambda=3.736772 
## - Fold09.Rep1: alpha=0.3536, lambda=3.736772 
## + Fold09.Rep1: alpha=0.7569, lambda=0.457474 
## - Fold09.Rep1: alpha=0.7569, lambda=0.457474 
## + Fold09.Rep1: alpha=0.4423, lambda=0.004959 
## - Fold09.Rep1: alpha=0.4423, lambda=0.004959 
## + Fold09.Rep1: alpha=0.4111, lambda=0.885269 
## - Fold09.Rep1: alpha=0.4111, lambda=0.885269 
## + Fold09.Rep1: alpha=0.4419, lambda=0.014470 
## - Fold09.Rep1: alpha=0.4419, lambda=0.014470 
## + Fold09.Rep1: alpha=0.2539, lambda=6.506213 
## - Fold09.Rep1: alpha=0.2539, lambda=6.506213 
## + Fold10.Rep1: alpha=0.7034, lambda=0.215777 
## - Fold10.Rep1: alpha=0.7034, lambda=0.215777 
## + Fold10.Rep1: alpha=0.1303, lambda=2.918438 
## - Fold10.Rep1: alpha=0.1303, lambda=2.918438 
## + Fold10.Rep1: alpha=0.9303, lambda=0.013567 
## - Fold10.Rep1: alpha=0.9303, lambda=0.013567 
## + Fold10.Rep1: alpha=0.9076, lambda=3.206257 
## - Fold10.Rep1: alpha=0.9076, lambda=3.206257 
## + Fold10.Rep1: alpha=0.3536, lambda=3.736772 
## - Fold10.Rep1: alpha=0.3536, lambda=3.736772 
## + Fold10.Rep1: alpha=0.7569, lambda=0.457474 
## - Fold10.Rep1: alpha=0.7569, lambda=0.457474 
## + Fold10.Rep1: alpha=0.4423, lambda=0.004959 
## - Fold10.Rep1: alpha=0.4423, lambda=0.004959 
## + Fold10.Rep1: alpha=0.4111, lambda=0.885269 
## - Fold10.Rep1: alpha=0.4111, lambda=0.885269 
## + Fold10.Rep1: alpha=0.4419, lambda=0.014470 
## - Fold10.Rep1: alpha=0.4419, lambda=0.014470 
## + Fold10.Rep1: alpha=0.2539, lambda=6.506213 
## - Fold10.Rep1: alpha=0.2539, lambda=6.506213 
## + Fold01.Rep2: alpha=0.7034, lambda=0.215777 
## - Fold01.Rep2: alpha=0.7034, lambda=0.215777 
## + Fold01.Rep2: alpha=0.1303, lambda=2.918438 
## - Fold01.Rep2: alpha=0.1303, lambda=2.918438 
## + Fold01.Rep2: alpha=0.9303, lambda=0.013567 
## - Fold01.Rep2: alpha=0.9303, lambda=0.013567 
## + Fold01.Rep2: alpha=0.9076, lambda=3.206257 
## - Fold01.Rep2: alpha=0.9076, lambda=3.206257 
## + Fold01.Rep2: alpha=0.3536, lambda=3.736772 
## - Fold01.Rep2: alpha=0.3536, lambda=3.736772 
## + Fold01.Rep2: alpha=0.7569, lambda=0.457474 
## - Fold01.Rep2: alpha=0.7569, lambda=0.457474 
## + Fold01.Rep2: alpha=0.4423, lambda=0.004959 
## - Fold01.Rep2: alpha=0.4423, lambda=0.004959 
## + Fold01.Rep2: alpha=0.4111, lambda=0.885269 
## - Fold01.Rep2: alpha=0.4111, lambda=0.885269 
## + Fold01.Rep2: alpha=0.4419, lambda=0.014470 
## - Fold01.Rep2: alpha=0.4419, lambda=0.014470 
## + Fold01.Rep2: alpha=0.2539, lambda=6.506213 
## - Fold01.Rep2: alpha=0.2539, lambda=6.506213 
## + Fold02.Rep2: alpha=0.7034, lambda=0.215777 
## - Fold02.Rep2: alpha=0.7034, lambda=0.215777 
## + Fold02.Rep2: alpha=0.1303, lambda=2.918438 
## - Fold02.Rep2: alpha=0.1303, lambda=2.918438 
## + Fold02.Rep2: alpha=0.9303, lambda=0.013567 
## - Fold02.Rep2: alpha=0.9303, lambda=0.013567 
## + Fold02.Rep2: alpha=0.9076, lambda=3.206257 
## - Fold02.Rep2: alpha=0.9076, lambda=3.206257 
## + Fold02.Rep2: alpha=0.3536, lambda=3.736772 
## - Fold02.Rep2: alpha=0.3536, lambda=3.736772 
## + Fold02.Rep2: alpha=0.7569, lambda=0.457474 
## - Fold02.Rep2: alpha=0.7569, lambda=0.457474 
## + Fold02.Rep2: alpha=0.4423, lambda=0.004959 
## - Fold02.Rep2: alpha=0.4423, lambda=0.004959 
## + Fold02.Rep2: alpha=0.4111, lambda=0.885269 
## - Fold02.Rep2: alpha=0.4111, lambda=0.885269 
## + Fold02.Rep2: alpha=0.4419, lambda=0.014470 
## - Fold02.Rep2: alpha=0.4419, lambda=0.014470 
## + Fold02.Rep2: alpha=0.2539, lambda=6.506213 
## - Fold02.Rep2: alpha=0.2539, lambda=6.506213 
## + Fold03.Rep2: alpha=0.7034, lambda=0.215777 
## - Fold03.Rep2: alpha=0.7034, lambda=0.215777 
## + Fold03.Rep2: alpha=0.1303, lambda=2.918438 
## - Fold03.Rep2: alpha=0.1303, lambda=2.918438 
## + Fold03.Rep2: alpha=0.9303, lambda=0.013567 
## - Fold03.Rep2: alpha=0.9303, lambda=0.013567 
## + Fold03.Rep2: alpha=0.9076, lambda=3.206257 
## - Fold03.Rep2: alpha=0.9076, lambda=3.206257 
## + Fold03.Rep2: alpha=0.3536, lambda=3.736772 
## - Fold03.Rep2: alpha=0.3536, lambda=3.736772 
## + Fold03.Rep2: alpha=0.7569, lambda=0.457474 
## - Fold03.Rep2: alpha=0.7569, lambda=0.457474 
## + Fold03.Rep2: alpha=0.4423, lambda=0.004959 
## - Fold03.Rep2: alpha=0.4423, lambda=0.004959 
## + Fold03.Rep2: alpha=0.4111, lambda=0.885269 
## - Fold03.Rep2: alpha=0.4111, lambda=0.885269 
## + Fold03.Rep2: alpha=0.4419, lambda=0.014470 
## - Fold03.Rep2: alpha=0.4419, lambda=0.014470 
## + Fold03.Rep2: alpha=0.2539, lambda=6.506213 
## - Fold03.Rep2: alpha=0.2539, lambda=6.506213 
## + Fold04.Rep2: alpha=0.7034, lambda=0.215777 
## - Fold04.Rep2: alpha=0.7034, lambda=0.215777 
## + Fold04.Rep2: alpha=0.1303, lambda=2.918438 
## - Fold04.Rep2: alpha=0.1303, lambda=2.918438 
## + Fold04.Rep2: alpha=0.9303, lambda=0.013567 
## - Fold04.Rep2: alpha=0.9303, lambda=0.013567 
## + Fold04.Rep2: alpha=0.9076, lambda=3.206257 
## - Fold04.Rep2: alpha=0.9076, lambda=3.206257 
## + Fold04.Rep2: alpha=0.3536, lambda=3.736772 
## - Fold04.Rep2: alpha=0.3536, lambda=3.736772 
## + Fold04.Rep2: alpha=0.7569, lambda=0.457474 
## - Fold04.Rep2: alpha=0.7569, lambda=0.457474 
## + Fold04.Rep2: alpha=0.4423, lambda=0.004959 
## - Fold04.Rep2: alpha=0.4423, lambda=0.004959 
## + Fold04.Rep2: alpha=0.4111, lambda=0.885269 
## - Fold04.Rep2: alpha=0.4111, lambda=0.885269 
## + Fold04.Rep2: alpha=0.4419, lambda=0.014470 
## - Fold04.Rep2: alpha=0.4419, lambda=0.014470 
## + Fold04.Rep2: alpha=0.2539, lambda=6.506213 
## - Fold04.Rep2: alpha=0.2539, lambda=6.506213 
## + Fold05.Rep2: alpha=0.7034, lambda=0.215777 
## - Fold05.Rep2: alpha=0.7034, lambda=0.215777 
## + Fold05.Rep2: alpha=0.1303, lambda=2.918438 
## - Fold05.Rep2: alpha=0.1303, lambda=2.918438 
## + Fold05.Rep2: alpha=0.9303, lambda=0.013567 
## - Fold05.Rep2: alpha=0.9303, lambda=0.013567 
## + Fold05.Rep2: alpha=0.9076, lambda=3.206257 
## - Fold05.Rep2: alpha=0.9076, lambda=3.206257 
## + Fold05.Rep2: alpha=0.3536, lambda=3.736772 
## - Fold05.Rep2: alpha=0.3536, lambda=3.736772 
## + Fold05.Rep2: alpha=0.7569, lambda=0.457474 
## - Fold05.Rep2: alpha=0.7569, lambda=0.457474 
## + Fold05.Rep2: alpha=0.4423, lambda=0.004959 
## - Fold05.Rep2: alpha=0.4423, lambda=0.004959 
## + Fold05.Rep2: alpha=0.4111, lambda=0.885269 
## - Fold05.Rep2: alpha=0.4111, lambda=0.885269 
## + Fold05.Rep2: alpha=0.4419, lambda=0.014470 
## - Fold05.Rep2: alpha=0.4419, lambda=0.014470 
## + Fold05.Rep2: alpha=0.2539, lambda=6.506213 
## - Fold05.Rep2: alpha=0.2539, lambda=6.506213 
## + Fold06.Rep2: alpha=0.7034, lambda=0.215777 
## - Fold06.Rep2: alpha=0.7034, lambda=0.215777 
## + Fold06.Rep2: alpha=0.1303, lambda=2.918438 
## - Fold06.Rep2: alpha=0.1303, lambda=2.918438 
## + Fold06.Rep2: alpha=0.9303, lambda=0.013567 
## - Fold06.Rep2: alpha=0.9303, lambda=0.013567 
## + Fold06.Rep2: alpha=0.9076, lambda=3.206257 
## - Fold06.Rep2: alpha=0.9076, lambda=3.206257 
## + Fold06.Rep2: alpha=0.3536, lambda=3.736772 
## - Fold06.Rep2: alpha=0.3536, lambda=3.736772 
## + Fold06.Rep2: alpha=0.7569, lambda=0.457474 
## - Fold06.Rep2: alpha=0.7569, lambda=0.457474 
## + Fold06.Rep2: alpha=0.4423, lambda=0.004959 
## - Fold06.Rep2: alpha=0.4423, lambda=0.004959 
## + Fold06.Rep2: alpha=0.4111, lambda=0.885269 
## - Fold06.Rep2: alpha=0.4111, lambda=0.885269 
## + Fold06.Rep2: alpha=0.4419, lambda=0.014470 
## - Fold06.Rep2: alpha=0.4419, lambda=0.014470 
## + Fold06.Rep2: alpha=0.2539, lambda=6.506213 
## - Fold06.Rep2: alpha=0.2539, lambda=6.506213 
## + Fold07.Rep2: alpha=0.7034, lambda=0.215777 
## - Fold07.Rep2: alpha=0.7034, lambda=0.215777 
## + Fold07.Rep2: alpha=0.1303, lambda=2.918438 
## - Fold07.Rep2: alpha=0.1303, lambda=2.918438 
## + Fold07.Rep2: alpha=0.9303, lambda=0.013567 
## - Fold07.Rep2: alpha=0.9303, lambda=0.013567 
## + Fold07.Rep2: alpha=0.9076, lambda=3.206257 
## - Fold07.Rep2: alpha=0.9076, lambda=3.206257 
## + Fold07.Rep2: alpha=0.3536, lambda=3.736772 
## - Fold07.Rep2: alpha=0.3536, lambda=3.736772 
## + Fold07.Rep2: alpha=0.7569, lambda=0.457474 
## - Fold07.Rep2: alpha=0.7569, lambda=0.457474 
## + Fold07.Rep2: alpha=0.4423, lambda=0.004959 
## - Fold07.Rep2: alpha=0.4423, lambda=0.004959 
## + Fold07.Rep2: alpha=0.4111, lambda=0.885269 
## - Fold07.Rep2: alpha=0.4111, lambda=0.885269 
## + Fold07.Rep2: alpha=0.4419, lambda=0.014470 
## - Fold07.Rep2: alpha=0.4419, lambda=0.014470 
## + Fold07.Rep2: alpha=0.2539, lambda=6.506213 
## - Fold07.Rep2: alpha=0.2539, lambda=6.506213 
## + Fold08.Rep2: alpha=0.7034, lambda=0.215777 
## - Fold08.Rep2: alpha=0.7034, lambda=0.215777 
## + Fold08.Rep2: alpha=0.1303, lambda=2.918438 
## - Fold08.Rep2: alpha=0.1303, lambda=2.918438 
## + Fold08.Rep2: alpha=0.9303, lambda=0.013567 
## - Fold08.Rep2: alpha=0.9303, lambda=0.013567 
## + Fold08.Rep2: alpha=0.9076, lambda=3.206257 
## - Fold08.Rep2: alpha=0.9076, lambda=3.206257 
## + Fold08.Rep2: alpha=0.3536, lambda=3.736772 
## - Fold08.Rep2: alpha=0.3536, lambda=3.736772 
## + Fold08.Rep2: alpha=0.7569, lambda=0.457474 
## - Fold08.Rep2: alpha=0.7569, lambda=0.457474 
## + Fold08.Rep2: alpha=0.4423, lambda=0.004959 
## - Fold08.Rep2: alpha=0.4423, lambda=0.004959 
## + Fold08.Rep2: alpha=0.4111, lambda=0.885269 
## - Fold08.Rep2: alpha=0.4111, lambda=0.885269 
## + Fold08.Rep2: alpha=0.4419, lambda=0.014470 
## - Fold08.Rep2: alpha=0.4419, lambda=0.014470 
## + Fold08.Rep2: alpha=0.2539, lambda=6.506213 
## - Fold08.Rep2: alpha=0.2539, lambda=6.506213 
## + Fold09.Rep2: alpha=0.7034, lambda=0.215777 
## - Fold09.Rep2: alpha=0.7034, lambda=0.215777 
## + Fold09.Rep2: alpha=0.1303, lambda=2.918438 
## - Fold09.Rep2: alpha=0.1303, lambda=2.918438 
## + Fold09.Rep2: alpha=0.9303, lambda=0.013567 
## - Fold09.Rep2: alpha=0.9303, lambda=0.013567 
## + Fold09.Rep2: alpha=0.9076, lambda=3.206257 
## - Fold09.Rep2: alpha=0.9076, lambda=3.206257 
## + Fold09.Rep2: alpha=0.3536, lambda=3.736772 
## - Fold09.Rep2: alpha=0.3536, lambda=3.736772 
## + Fold09.Rep2: alpha=0.7569, lambda=0.457474 
## - Fold09.Rep2: alpha=0.7569, lambda=0.457474 
## + Fold09.Rep2: alpha=0.4423, lambda=0.004959 
## - Fold09.Rep2: alpha=0.4423, lambda=0.004959 
## + Fold09.Rep2: alpha=0.4111, lambda=0.885269 
## - Fold09.Rep2: alpha=0.4111, lambda=0.885269 
## + Fold09.Rep2: alpha=0.4419, lambda=0.014470 
## - Fold09.Rep2: alpha=0.4419, lambda=0.014470 
## + Fold09.Rep2: alpha=0.2539, lambda=6.506213 
## - Fold09.Rep2: alpha=0.2539, lambda=6.506213 
## + Fold10.Rep2: alpha=0.7034, lambda=0.215777 
## - Fold10.Rep2: alpha=0.7034, lambda=0.215777 
## + Fold10.Rep2: alpha=0.1303, lambda=2.918438 
## - Fold10.Rep2: alpha=0.1303, lambda=2.918438 
## + Fold10.Rep2: alpha=0.9303, lambda=0.013567 
## - Fold10.Rep2: alpha=0.9303, lambda=0.013567 
## + Fold10.Rep2: alpha=0.9076, lambda=3.206257 
## - Fold10.Rep2: alpha=0.9076, lambda=3.206257 
## + Fold10.Rep2: alpha=0.3536, lambda=3.736772 
## - Fold10.Rep2: alpha=0.3536, lambda=3.736772 
## + Fold10.Rep2: alpha=0.7569, lambda=0.457474 
## - Fold10.Rep2: alpha=0.7569, lambda=0.457474 
## + Fold10.Rep2: alpha=0.4423, lambda=0.004959 
## - Fold10.Rep2: alpha=0.4423, lambda=0.004959 
## + Fold10.Rep2: alpha=0.4111, lambda=0.885269 
## - Fold10.Rep2: alpha=0.4111, lambda=0.885269 
## + Fold10.Rep2: alpha=0.4419, lambda=0.014470 
## - Fold10.Rep2: alpha=0.4419, lambda=0.014470 
## + Fold10.Rep2: alpha=0.2539, lambda=6.506213 
## - Fold10.Rep2: alpha=0.2539, lambda=6.506213 
## + Fold01.Rep3: alpha=0.7034, lambda=0.215777 
## - Fold01.Rep3: alpha=0.7034, lambda=0.215777 
## + Fold01.Rep3: alpha=0.1303, lambda=2.918438 
## - Fold01.Rep3: alpha=0.1303, lambda=2.918438 
## + Fold01.Rep3: alpha=0.9303, lambda=0.013567 
## - Fold01.Rep3: alpha=0.9303, lambda=0.013567 
## + Fold01.Rep3: alpha=0.9076, lambda=3.206257 
## - Fold01.Rep3: alpha=0.9076, lambda=3.206257 
## + Fold01.Rep3: alpha=0.3536, lambda=3.736772 
## - Fold01.Rep3: alpha=0.3536, lambda=3.736772 
## + Fold01.Rep3: alpha=0.7569, lambda=0.457474 
## - Fold01.Rep3: alpha=0.7569, lambda=0.457474 
## + Fold01.Rep3: alpha=0.4423, lambda=0.004959 
## - Fold01.Rep3: alpha=0.4423, lambda=0.004959 
## + Fold01.Rep3: alpha=0.4111, lambda=0.885269 
## - Fold01.Rep3: alpha=0.4111, lambda=0.885269 
## + Fold01.Rep3: alpha=0.4419, lambda=0.014470 
## - Fold01.Rep3: alpha=0.4419, lambda=0.014470 
## + Fold01.Rep3: alpha=0.2539, lambda=6.506213 
## - Fold01.Rep3: alpha=0.2539, lambda=6.506213 
## + Fold02.Rep3: alpha=0.7034, lambda=0.215777 
## - Fold02.Rep3: alpha=0.7034, lambda=0.215777 
## + Fold02.Rep3: alpha=0.1303, lambda=2.918438 
## - Fold02.Rep3: alpha=0.1303, lambda=2.918438 
## + Fold02.Rep3: alpha=0.9303, lambda=0.013567 
## - Fold02.Rep3: alpha=0.9303, lambda=0.013567 
## + Fold02.Rep3: alpha=0.9076, lambda=3.206257 
## - Fold02.Rep3: alpha=0.9076, lambda=3.206257 
## + Fold02.Rep3: alpha=0.3536, lambda=3.736772 
## - Fold02.Rep3: alpha=0.3536, lambda=3.736772 
## + Fold02.Rep3: alpha=0.7569, lambda=0.457474 
## - Fold02.Rep3: alpha=0.7569, lambda=0.457474 
## + Fold02.Rep3: alpha=0.4423, lambda=0.004959 
## - Fold02.Rep3: alpha=0.4423, lambda=0.004959 
## + Fold02.Rep3: alpha=0.4111, lambda=0.885269 
## - Fold02.Rep3: alpha=0.4111, lambda=0.885269 
## + Fold02.Rep3: alpha=0.4419, lambda=0.014470 
## - Fold02.Rep3: alpha=0.4419, lambda=0.014470 
## + Fold02.Rep3: alpha=0.2539, lambda=6.506213 
## - Fold02.Rep3: alpha=0.2539, lambda=6.506213 
## + Fold03.Rep3: alpha=0.7034, lambda=0.215777 
## - Fold03.Rep3: alpha=0.7034, lambda=0.215777 
## + Fold03.Rep3: alpha=0.1303, lambda=2.918438 
## - Fold03.Rep3: alpha=0.1303, lambda=2.918438 
## + Fold03.Rep3: alpha=0.9303, lambda=0.013567 
## - Fold03.Rep3: alpha=0.9303, lambda=0.013567 
## + Fold03.Rep3: alpha=0.9076, lambda=3.206257 
## - Fold03.Rep3: alpha=0.9076, lambda=3.206257 
## + Fold03.Rep3: alpha=0.3536, lambda=3.736772 
## - Fold03.Rep3: alpha=0.3536, lambda=3.736772 
## + Fold03.Rep3: alpha=0.7569, lambda=0.457474 
## - Fold03.Rep3: alpha=0.7569, lambda=0.457474 
## + Fold03.Rep3: alpha=0.4423, lambda=0.004959 
## - Fold03.Rep3: alpha=0.4423, lambda=0.004959 
## + Fold03.Rep3: alpha=0.4111, lambda=0.885269 
## - Fold03.Rep3: alpha=0.4111, lambda=0.885269 
## + Fold03.Rep3: alpha=0.4419, lambda=0.014470 
## - Fold03.Rep3: alpha=0.4419, lambda=0.014470 
## + Fold03.Rep3: alpha=0.2539, lambda=6.506213 
## - Fold03.Rep3: alpha=0.2539, lambda=6.506213 
## + Fold04.Rep3: alpha=0.7034, lambda=0.215777 
## - Fold04.Rep3: alpha=0.7034, lambda=0.215777 
## + Fold04.Rep3: alpha=0.1303, lambda=2.918438 
## - Fold04.Rep3: alpha=0.1303, lambda=2.918438 
## + Fold04.Rep3: alpha=0.9303, lambda=0.013567 
## - Fold04.Rep3: alpha=0.9303, lambda=0.013567 
## + Fold04.Rep3: alpha=0.9076, lambda=3.206257 
## - Fold04.Rep3: alpha=0.9076, lambda=3.206257 
## + Fold04.Rep3: alpha=0.3536, lambda=3.736772 
## - Fold04.Rep3: alpha=0.3536, lambda=3.736772 
## + Fold04.Rep3: alpha=0.7569, lambda=0.457474 
## - Fold04.Rep3: alpha=0.7569, lambda=0.457474 
## + Fold04.Rep3: alpha=0.4423, lambda=0.004959 
## - Fold04.Rep3: alpha=0.4423, lambda=0.004959 
## + Fold04.Rep3: alpha=0.4111, lambda=0.885269 
## - Fold04.Rep3: alpha=0.4111, lambda=0.885269 
## + Fold04.Rep3: alpha=0.4419, lambda=0.014470 
## - Fold04.Rep3: alpha=0.4419, lambda=0.014470 
## + Fold04.Rep3: alpha=0.2539, lambda=6.506213 
## - Fold04.Rep3: alpha=0.2539, lambda=6.506213 
## + Fold05.Rep3: alpha=0.7034, lambda=0.215777 
## - Fold05.Rep3: alpha=0.7034, lambda=0.215777 
## + Fold05.Rep3: alpha=0.1303, lambda=2.918438 
## - Fold05.Rep3: alpha=0.1303, lambda=2.918438 
## + Fold05.Rep3: alpha=0.9303, lambda=0.013567 
## - Fold05.Rep3: alpha=0.9303, lambda=0.013567 
## + Fold05.Rep3: alpha=0.9076, lambda=3.206257 
## - Fold05.Rep3: alpha=0.9076, lambda=3.206257 
## + Fold05.Rep3: alpha=0.3536, lambda=3.736772 
## - Fold05.Rep3: alpha=0.3536, lambda=3.736772 
## + Fold05.Rep3: alpha=0.7569, lambda=0.457474 
## - Fold05.Rep3: alpha=0.7569, lambda=0.457474 
## + Fold05.Rep3: alpha=0.4423, lambda=0.004959 
## - Fold05.Rep3: alpha=0.4423, lambda=0.004959 
## + Fold05.Rep3: alpha=0.4111, lambda=0.885269 
## - Fold05.Rep3: alpha=0.4111, lambda=0.885269 
## + Fold05.Rep3: alpha=0.4419, lambda=0.014470 
## - Fold05.Rep3: alpha=0.4419, lambda=0.014470 
## + Fold05.Rep3: alpha=0.2539, lambda=6.506213 
## - Fold05.Rep3: alpha=0.2539, lambda=6.506213 
## + Fold06.Rep3: alpha=0.7034, lambda=0.215777 
## - Fold06.Rep3: alpha=0.7034, lambda=0.215777 
## + Fold06.Rep3: alpha=0.1303, lambda=2.918438 
## - Fold06.Rep3: alpha=0.1303, lambda=2.918438 
## + Fold06.Rep3: alpha=0.9303, lambda=0.013567 
## - Fold06.Rep3: alpha=0.9303, lambda=0.013567 
## + Fold06.Rep3: alpha=0.9076, lambda=3.206257 
## - Fold06.Rep3: alpha=0.9076, lambda=3.206257 
## + Fold06.Rep3: alpha=0.3536, lambda=3.736772 
## - Fold06.Rep3: alpha=0.3536, lambda=3.736772 
## + Fold06.Rep3: alpha=0.7569, lambda=0.457474 
## - Fold06.Rep3: alpha=0.7569, lambda=0.457474 
## + Fold06.Rep3: alpha=0.4423, lambda=0.004959 
## - Fold06.Rep3: alpha=0.4423, lambda=0.004959 
## + Fold06.Rep3: alpha=0.4111, lambda=0.885269 
## - Fold06.Rep3: alpha=0.4111, lambda=0.885269 
## + Fold06.Rep3: alpha=0.4419, lambda=0.014470 
## - Fold06.Rep3: alpha=0.4419, lambda=0.014470 
## + Fold06.Rep3: alpha=0.2539, lambda=6.506213 
## - Fold06.Rep3: alpha=0.2539, lambda=6.506213 
## + Fold07.Rep3: alpha=0.7034, lambda=0.215777 
## - Fold07.Rep3: alpha=0.7034, lambda=0.215777 
## + Fold07.Rep3: alpha=0.1303, lambda=2.918438 
## - Fold07.Rep3: alpha=0.1303, lambda=2.918438 
## + Fold07.Rep3: alpha=0.9303, lambda=0.013567 
## - Fold07.Rep3: alpha=0.9303, lambda=0.013567 
## + Fold07.Rep3: alpha=0.9076, lambda=3.206257 
## - Fold07.Rep3: alpha=0.9076, lambda=3.206257 
## + Fold07.Rep3: alpha=0.3536, lambda=3.736772 
## - Fold07.Rep3: alpha=0.3536, lambda=3.736772 
## + Fold07.Rep3: alpha=0.7569, lambda=0.457474 
## - Fold07.Rep3: alpha=0.7569, lambda=0.457474 
## + Fold07.Rep3: alpha=0.4423, lambda=0.004959 
## - Fold07.Rep3: alpha=0.4423, lambda=0.004959 
## + Fold07.Rep3: alpha=0.4111, lambda=0.885269 
## - Fold07.Rep3: alpha=0.4111, lambda=0.885269 
## + Fold07.Rep3: alpha=0.4419, lambda=0.014470 
## - Fold07.Rep3: alpha=0.4419, lambda=0.014470 
## + Fold07.Rep3: alpha=0.2539, lambda=6.506213 
## - Fold07.Rep3: alpha=0.2539, lambda=6.506213 
## + Fold08.Rep3: alpha=0.7034, lambda=0.215777 
## - Fold08.Rep3: alpha=0.7034, lambda=0.215777 
## + Fold08.Rep3: alpha=0.1303, lambda=2.918438 
## - Fold08.Rep3: alpha=0.1303, lambda=2.918438 
## + Fold08.Rep3: alpha=0.9303, lambda=0.013567 
## - Fold08.Rep3: alpha=0.9303, lambda=0.013567 
## + Fold08.Rep3: alpha=0.9076, lambda=3.206257 
## - Fold08.Rep3: alpha=0.9076, lambda=3.206257 
## + Fold08.Rep3: alpha=0.3536, lambda=3.736772 
## - Fold08.Rep3: alpha=0.3536, lambda=3.736772 
## + Fold08.Rep3: alpha=0.7569, lambda=0.457474 
## - Fold08.Rep3: alpha=0.7569, lambda=0.457474 
## + Fold08.Rep3: alpha=0.4423, lambda=0.004959 
## - Fold08.Rep3: alpha=0.4423, lambda=0.004959 
## + Fold08.Rep3: alpha=0.4111, lambda=0.885269 
## - Fold08.Rep3: alpha=0.4111, lambda=0.885269 
## + Fold08.Rep3: alpha=0.4419, lambda=0.014470 
## - Fold08.Rep3: alpha=0.4419, lambda=0.014470 
## + Fold08.Rep3: alpha=0.2539, lambda=6.506213 
## - Fold08.Rep3: alpha=0.2539, lambda=6.506213 
## + Fold09.Rep3: alpha=0.7034, lambda=0.215777 
## - Fold09.Rep3: alpha=0.7034, lambda=0.215777 
## + Fold09.Rep3: alpha=0.1303, lambda=2.918438 
## - Fold09.Rep3: alpha=0.1303, lambda=2.918438 
## + Fold09.Rep3: alpha=0.9303, lambda=0.013567 
## - Fold09.Rep3: alpha=0.9303, lambda=0.013567 
## + Fold09.Rep3: alpha=0.9076, lambda=3.206257 
## - Fold09.Rep3: alpha=0.9076, lambda=3.206257 
## + Fold09.Rep3: alpha=0.3536, lambda=3.736772 
## - Fold09.Rep3: alpha=0.3536, lambda=3.736772 
## + Fold09.Rep3: alpha=0.7569, lambda=0.457474 
## - Fold09.Rep3: alpha=0.7569, lambda=0.457474 
## + Fold09.Rep3: alpha=0.4423, lambda=0.004959 
## - Fold09.Rep3: alpha=0.4423, lambda=0.004959 
## + Fold09.Rep3: alpha=0.4111, lambda=0.885269 
## - Fold09.Rep3: alpha=0.4111, lambda=0.885269 
## + Fold09.Rep3: alpha=0.4419, lambda=0.014470 
## - Fold09.Rep3: alpha=0.4419, lambda=0.014470 
## + Fold09.Rep3: alpha=0.2539, lambda=6.506213 
## - Fold09.Rep3: alpha=0.2539, lambda=6.506213 
## + Fold10.Rep3: alpha=0.7034, lambda=0.215777 
## - Fold10.Rep3: alpha=0.7034, lambda=0.215777 
## + Fold10.Rep3: alpha=0.1303, lambda=2.918438 
## - Fold10.Rep3: alpha=0.1303, lambda=2.918438 
## + Fold10.Rep3: alpha=0.9303, lambda=0.013567 
## - Fold10.Rep3: alpha=0.9303, lambda=0.013567 
## + Fold10.Rep3: alpha=0.9076, lambda=3.206257 
## - Fold10.Rep3: alpha=0.9076, lambda=3.206257 
## + Fold10.Rep3: alpha=0.3536, lambda=3.736772 
## - Fold10.Rep3: alpha=0.3536, lambda=3.736772 
## + Fold10.Rep3: alpha=0.7569, lambda=0.457474 
## - Fold10.Rep3: alpha=0.7569, lambda=0.457474 
## + Fold10.Rep3: alpha=0.4423, lambda=0.004959 
## - Fold10.Rep3: alpha=0.4423, lambda=0.004959 
## + Fold10.Rep3: alpha=0.4111, lambda=0.885269 
## - Fold10.Rep3: alpha=0.4111, lambda=0.885269 
## + Fold10.Rep3: alpha=0.4419, lambda=0.014470 
## - Fold10.Rep3: alpha=0.4419, lambda=0.014470 
## + Fold10.Rep3: alpha=0.2539, lambda=6.506213 
## - Fold10.Rep3: alpha=0.2539, lambda=6.506213 
## + Fold01.Rep4: alpha=0.7034, lambda=0.215777 
## - Fold01.Rep4: alpha=0.7034, lambda=0.215777 
## + Fold01.Rep4: alpha=0.1303, lambda=2.918438 
## - Fold01.Rep4: alpha=0.1303, lambda=2.918438 
## + Fold01.Rep4: alpha=0.9303, lambda=0.013567 
## - Fold01.Rep4: alpha=0.9303, lambda=0.013567 
## + Fold01.Rep4: alpha=0.9076, lambda=3.206257 
## - Fold01.Rep4: alpha=0.9076, lambda=3.206257 
## + Fold01.Rep4: alpha=0.3536, lambda=3.736772 
## - Fold01.Rep4: alpha=0.3536, lambda=3.736772 
## + Fold01.Rep4: alpha=0.7569, lambda=0.457474 
## - Fold01.Rep4: alpha=0.7569, lambda=0.457474 
## + Fold01.Rep4: alpha=0.4423, lambda=0.004959 
## - Fold01.Rep4: alpha=0.4423, lambda=0.004959 
## + Fold01.Rep4: alpha=0.4111, lambda=0.885269 
## - Fold01.Rep4: alpha=0.4111, lambda=0.885269 
## + Fold01.Rep4: alpha=0.4419, lambda=0.014470 
## - Fold01.Rep4: alpha=0.4419, lambda=0.014470 
## + Fold01.Rep4: alpha=0.2539, lambda=6.506213 
## - Fold01.Rep4: alpha=0.2539, lambda=6.506213 
## + Fold02.Rep4: alpha=0.7034, lambda=0.215777 
## - Fold02.Rep4: alpha=0.7034, lambda=0.215777 
## + Fold02.Rep4: alpha=0.1303, lambda=2.918438 
## - Fold02.Rep4: alpha=0.1303, lambda=2.918438 
## + Fold02.Rep4: alpha=0.9303, lambda=0.013567 
## - Fold02.Rep4: alpha=0.9303, lambda=0.013567 
## + Fold02.Rep4: alpha=0.9076, lambda=3.206257 
## - Fold02.Rep4: alpha=0.9076, lambda=3.206257 
## + Fold02.Rep4: alpha=0.3536, lambda=3.736772 
## - Fold02.Rep4: alpha=0.3536, lambda=3.736772 
## + Fold02.Rep4: alpha=0.7569, lambda=0.457474 
## - Fold02.Rep4: alpha=0.7569, lambda=0.457474 
## + Fold02.Rep4: alpha=0.4423, lambda=0.004959 
## - Fold02.Rep4: alpha=0.4423, lambda=0.004959 
## + Fold02.Rep4: alpha=0.4111, lambda=0.885269 
## - Fold02.Rep4: alpha=0.4111, lambda=0.885269 
## + Fold02.Rep4: alpha=0.4419, lambda=0.014470 
## - Fold02.Rep4: alpha=0.4419, lambda=0.014470 
## + Fold02.Rep4: alpha=0.2539, lambda=6.506213 
## - Fold02.Rep4: alpha=0.2539, lambda=6.506213 
## + Fold03.Rep4: alpha=0.7034, lambda=0.215777 
## - Fold03.Rep4: alpha=0.7034, lambda=0.215777 
## + Fold03.Rep4: alpha=0.1303, lambda=2.918438 
## - Fold03.Rep4: alpha=0.1303, lambda=2.918438 
## + Fold03.Rep4: alpha=0.9303, lambda=0.013567 
## - Fold03.Rep4: alpha=0.9303, lambda=0.013567 
## + Fold03.Rep4: alpha=0.9076, lambda=3.206257 
## - Fold03.Rep4: alpha=0.9076, lambda=3.206257 
## + Fold03.Rep4: alpha=0.3536, lambda=3.736772 
## - Fold03.Rep4: alpha=0.3536, lambda=3.736772 
## + Fold03.Rep4: alpha=0.7569, lambda=0.457474 
## - Fold03.Rep4: alpha=0.7569, lambda=0.457474 
## + Fold03.Rep4: alpha=0.4423, lambda=0.004959 
## - Fold03.Rep4: alpha=0.4423, lambda=0.004959 
## + Fold03.Rep4: alpha=0.4111, lambda=0.885269 
## - Fold03.Rep4: alpha=0.4111, lambda=0.885269 
## + Fold03.Rep4: alpha=0.4419, lambda=0.014470 
## - Fold03.Rep4: alpha=0.4419, lambda=0.014470 
## + Fold03.Rep4: alpha=0.2539, lambda=6.506213 
## - Fold03.Rep4: alpha=0.2539, lambda=6.506213 
## + Fold04.Rep4: alpha=0.7034, lambda=0.215777 
## - Fold04.Rep4: alpha=0.7034, lambda=0.215777 
## + Fold04.Rep4: alpha=0.1303, lambda=2.918438 
## - Fold04.Rep4: alpha=0.1303, lambda=2.918438 
## + Fold04.Rep4: alpha=0.9303, lambda=0.013567 
## - Fold04.Rep4: alpha=0.9303, lambda=0.013567 
## + Fold04.Rep4: alpha=0.9076, lambda=3.206257 
## - Fold04.Rep4: alpha=0.9076, lambda=3.206257 
## + Fold04.Rep4: alpha=0.3536, lambda=3.736772 
## - Fold04.Rep4: alpha=0.3536, lambda=3.736772 
## + Fold04.Rep4: alpha=0.7569, lambda=0.457474 
## - Fold04.Rep4: alpha=0.7569, lambda=0.457474 
## + Fold04.Rep4: alpha=0.4423, lambda=0.004959 
## - Fold04.Rep4: alpha=0.4423, lambda=0.004959 
## + Fold04.Rep4: alpha=0.4111, lambda=0.885269 
## - Fold04.Rep4: alpha=0.4111, lambda=0.885269 
## + Fold04.Rep4: alpha=0.4419, lambda=0.014470 
## - Fold04.Rep4: alpha=0.4419, lambda=0.014470 
## + Fold04.Rep4: alpha=0.2539, lambda=6.506213 
## - Fold04.Rep4: alpha=0.2539, lambda=6.506213 
## + Fold05.Rep4: alpha=0.7034, lambda=0.215777 
## - Fold05.Rep4: alpha=0.7034, lambda=0.215777 
## + Fold05.Rep4: alpha=0.1303, lambda=2.918438 
## - Fold05.Rep4: alpha=0.1303, lambda=2.918438 
## + Fold05.Rep4: alpha=0.9303, lambda=0.013567 
## - Fold05.Rep4: alpha=0.9303, lambda=0.013567 
## + Fold05.Rep4: alpha=0.9076, lambda=3.206257 
## - Fold05.Rep4: alpha=0.9076, lambda=3.206257 
## + Fold05.Rep4: alpha=0.3536, lambda=3.736772 
## - Fold05.Rep4: alpha=0.3536, lambda=3.736772 
## + Fold05.Rep4: alpha=0.7569, lambda=0.457474 
## - Fold05.Rep4: alpha=0.7569, lambda=0.457474 
## + Fold05.Rep4: alpha=0.4423, lambda=0.004959 
## - Fold05.Rep4: alpha=0.4423, lambda=0.004959 
## + Fold05.Rep4: alpha=0.4111, lambda=0.885269 
## - Fold05.Rep4: alpha=0.4111, lambda=0.885269 
## + Fold05.Rep4: alpha=0.4419, lambda=0.014470 
## - Fold05.Rep4: alpha=0.4419, lambda=0.014470 
## + Fold05.Rep4: alpha=0.2539, lambda=6.506213 
## - Fold05.Rep4: alpha=0.2539, lambda=6.506213 
## + Fold06.Rep4: alpha=0.7034, lambda=0.215777 
## - Fold06.Rep4: alpha=0.7034, lambda=0.215777 
## + Fold06.Rep4: alpha=0.1303, lambda=2.918438 
## - Fold06.Rep4: alpha=0.1303, lambda=2.918438 
## + Fold06.Rep4: alpha=0.9303, lambda=0.013567 
## - Fold06.Rep4: alpha=0.9303, lambda=0.013567 
## + Fold06.Rep4: alpha=0.9076, lambda=3.206257 
## - Fold06.Rep4: alpha=0.9076, lambda=3.206257 
## + Fold06.Rep4: alpha=0.3536, lambda=3.736772 
## - Fold06.Rep4: alpha=0.3536, lambda=3.736772 
## + Fold06.Rep4: alpha=0.7569, lambda=0.457474 
## - Fold06.Rep4: alpha=0.7569, lambda=0.457474 
## + Fold06.Rep4: alpha=0.4423, lambda=0.004959 
## - Fold06.Rep4: alpha=0.4423, lambda=0.004959 
## + Fold06.Rep4: alpha=0.4111, lambda=0.885269 
## - Fold06.Rep4: alpha=0.4111, lambda=0.885269 
## + Fold06.Rep4: alpha=0.4419, lambda=0.014470 
## - Fold06.Rep4: alpha=0.4419, lambda=0.014470 
## + Fold06.Rep4: alpha=0.2539, lambda=6.506213 
## - Fold06.Rep4: alpha=0.2539, lambda=6.506213 
## + Fold07.Rep4: alpha=0.7034, lambda=0.215777 
## - Fold07.Rep4: alpha=0.7034, lambda=0.215777 
## + Fold07.Rep4: alpha=0.1303, lambda=2.918438 
## - Fold07.Rep4: alpha=0.1303, lambda=2.918438 
## + Fold07.Rep4: alpha=0.9303, lambda=0.013567 
## - Fold07.Rep4: alpha=0.9303, lambda=0.013567 
## + Fold07.Rep4: alpha=0.9076, lambda=3.206257 
## - Fold07.Rep4: alpha=0.9076, lambda=3.206257 
## + Fold07.Rep4: alpha=0.3536, lambda=3.736772 
## - Fold07.Rep4: alpha=0.3536, lambda=3.736772 
## + Fold07.Rep4: alpha=0.7569, lambda=0.457474 
## - Fold07.Rep4: alpha=0.7569, lambda=0.457474 
## + Fold07.Rep4: alpha=0.4423, lambda=0.004959 
## - Fold07.Rep4: alpha=0.4423, lambda=0.004959 
## + Fold07.Rep4: alpha=0.4111, lambda=0.885269 
## - Fold07.Rep4: alpha=0.4111, lambda=0.885269 
## + Fold07.Rep4: alpha=0.4419, lambda=0.014470 
## - Fold07.Rep4: alpha=0.4419, lambda=0.014470 
## + Fold07.Rep4: alpha=0.2539, lambda=6.506213 
## - Fold07.Rep4: alpha=0.2539, lambda=6.506213 
## + Fold08.Rep4: alpha=0.7034, lambda=0.215777 
## - Fold08.Rep4: alpha=0.7034, lambda=0.215777 
## + Fold08.Rep4: alpha=0.1303, lambda=2.918438 
## - Fold08.Rep4: alpha=0.1303, lambda=2.918438 
## + Fold08.Rep4: alpha=0.9303, lambda=0.013567 
## - Fold08.Rep4: alpha=0.9303, lambda=0.013567 
## + Fold08.Rep4: alpha=0.9076, lambda=3.206257 
## - Fold08.Rep4: alpha=0.9076, lambda=3.206257 
## + Fold08.Rep4: alpha=0.3536, lambda=3.736772 
## - Fold08.Rep4: alpha=0.3536, lambda=3.736772 
## + Fold08.Rep4: alpha=0.7569, lambda=0.457474 
## - Fold08.Rep4: alpha=0.7569, lambda=0.457474 
## + Fold08.Rep4: alpha=0.4423, lambda=0.004959 
## - Fold08.Rep4: alpha=0.4423, lambda=0.004959 
## + Fold08.Rep4: alpha=0.4111, lambda=0.885269 
## - Fold08.Rep4: alpha=0.4111, lambda=0.885269 
## + Fold08.Rep4: alpha=0.4419, lambda=0.014470 
## - Fold08.Rep4: alpha=0.4419, lambda=0.014470 
## + Fold08.Rep4: alpha=0.2539, lambda=6.506213 
## - Fold08.Rep4: alpha=0.2539, lambda=6.506213 
## + Fold09.Rep4: alpha=0.7034, lambda=0.215777 
## - Fold09.Rep4: alpha=0.7034, lambda=0.215777 
## + Fold09.Rep4: alpha=0.1303, lambda=2.918438 
## - Fold09.Rep4: alpha=0.1303, lambda=2.918438 
## + Fold09.Rep4: alpha=0.9303, lambda=0.013567 
## - Fold09.Rep4: alpha=0.9303, lambda=0.013567 
## + Fold09.Rep4: alpha=0.9076, lambda=3.206257 
## - Fold09.Rep4: alpha=0.9076, lambda=3.206257 
## + Fold09.Rep4: alpha=0.3536, lambda=3.736772 
## - Fold09.Rep4: alpha=0.3536, lambda=3.736772 
## + Fold09.Rep4: alpha=0.7569, lambda=0.457474 
## - Fold09.Rep4: alpha=0.7569, lambda=0.457474 
## + Fold09.Rep4: alpha=0.4423, lambda=0.004959 
## - Fold09.Rep4: alpha=0.4423, lambda=0.004959 
## + Fold09.Rep4: alpha=0.4111, lambda=0.885269 
## - Fold09.Rep4: alpha=0.4111, lambda=0.885269 
## + Fold09.Rep4: alpha=0.4419, lambda=0.014470 
## - Fold09.Rep4: alpha=0.4419, lambda=0.014470 
## + Fold09.Rep4: alpha=0.2539, lambda=6.506213 
## - Fold09.Rep4: alpha=0.2539, lambda=6.506213 
## + Fold10.Rep4: alpha=0.7034, lambda=0.215777 
## - Fold10.Rep4: alpha=0.7034, lambda=0.215777 
## + Fold10.Rep4: alpha=0.1303, lambda=2.918438 
## - Fold10.Rep4: alpha=0.1303, lambda=2.918438 
## + Fold10.Rep4: alpha=0.9303, lambda=0.013567 
## - Fold10.Rep4: alpha=0.9303, lambda=0.013567 
## + Fold10.Rep4: alpha=0.9076, lambda=3.206257 
## - Fold10.Rep4: alpha=0.9076, lambda=3.206257 
## + Fold10.Rep4: alpha=0.3536, lambda=3.736772 
## - Fold10.Rep4: alpha=0.3536, lambda=3.736772 
## + Fold10.Rep4: alpha=0.7569, lambda=0.457474 
## - Fold10.Rep4: alpha=0.7569, lambda=0.457474 
## + Fold10.Rep4: alpha=0.4423, lambda=0.004959 
## - Fold10.Rep4: alpha=0.4423, lambda=0.004959 
## + Fold10.Rep4: alpha=0.4111, lambda=0.885269 
## - Fold10.Rep4: alpha=0.4111, lambda=0.885269 
## + Fold10.Rep4: alpha=0.4419, lambda=0.014470 
## - Fold10.Rep4: alpha=0.4419, lambda=0.014470 
## + Fold10.Rep4: alpha=0.2539, lambda=6.506213 
## - Fold10.Rep4: alpha=0.2539, lambda=6.506213 
## + Fold01.Rep5: alpha=0.7034, lambda=0.215777 
## - Fold01.Rep5: alpha=0.7034, lambda=0.215777 
## + Fold01.Rep5: alpha=0.1303, lambda=2.918438 
## - Fold01.Rep5: alpha=0.1303, lambda=2.918438 
## + Fold01.Rep5: alpha=0.9303, lambda=0.013567 
## - Fold01.Rep5: alpha=0.9303, lambda=0.013567 
## + Fold01.Rep5: alpha=0.9076, lambda=3.206257 
## - Fold01.Rep5: alpha=0.9076, lambda=3.206257 
## + Fold01.Rep5: alpha=0.3536, lambda=3.736772 
## - Fold01.Rep5: alpha=0.3536, lambda=3.736772 
## + Fold01.Rep5: alpha=0.7569, lambda=0.457474 
## - Fold01.Rep5: alpha=0.7569, lambda=0.457474 
## + Fold01.Rep5: alpha=0.4423, lambda=0.004959 
## - Fold01.Rep5: alpha=0.4423, lambda=0.004959 
## + Fold01.Rep5: alpha=0.4111, lambda=0.885269 
## - Fold01.Rep5: alpha=0.4111, lambda=0.885269 
## + Fold01.Rep5: alpha=0.4419, lambda=0.014470 
## - Fold01.Rep5: alpha=0.4419, lambda=0.014470 
## + Fold01.Rep5: alpha=0.2539, lambda=6.506213 
## - Fold01.Rep5: alpha=0.2539, lambda=6.506213 
## + Fold02.Rep5: alpha=0.7034, lambda=0.215777 
## - Fold02.Rep5: alpha=0.7034, lambda=0.215777 
## + Fold02.Rep5: alpha=0.1303, lambda=2.918438 
## - Fold02.Rep5: alpha=0.1303, lambda=2.918438 
## + Fold02.Rep5: alpha=0.9303, lambda=0.013567 
## - Fold02.Rep5: alpha=0.9303, lambda=0.013567 
## + Fold02.Rep5: alpha=0.9076, lambda=3.206257 
## - Fold02.Rep5: alpha=0.9076, lambda=3.206257 
## + Fold02.Rep5: alpha=0.3536, lambda=3.736772 
## - Fold02.Rep5: alpha=0.3536, lambda=3.736772 
## + Fold02.Rep5: alpha=0.7569, lambda=0.457474 
## - Fold02.Rep5: alpha=0.7569, lambda=0.457474 
## + Fold02.Rep5: alpha=0.4423, lambda=0.004959 
## - Fold02.Rep5: alpha=0.4423, lambda=0.004959 
## + Fold02.Rep5: alpha=0.4111, lambda=0.885269 
## - Fold02.Rep5: alpha=0.4111, lambda=0.885269 
## + Fold02.Rep5: alpha=0.4419, lambda=0.014470 
## - Fold02.Rep5: alpha=0.4419, lambda=0.014470 
## + Fold02.Rep5: alpha=0.2539, lambda=6.506213 
## - Fold02.Rep5: alpha=0.2539, lambda=6.506213 
## + Fold03.Rep5: alpha=0.7034, lambda=0.215777 
## - Fold03.Rep5: alpha=0.7034, lambda=0.215777 
## + Fold03.Rep5: alpha=0.1303, lambda=2.918438 
## - Fold03.Rep5: alpha=0.1303, lambda=2.918438 
## + Fold03.Rep5: alpha=0.9303, lambda=0.013567 
## - Fold03.Rep5: alpha=0.9303, lambda=0.013567 
## + Fold03.Rep5: alpha=0.9076, lambda=3.206257 
## - Fold03.Rep5: alpha=0.9076, lambda=3.206257 
## + Fold03.Rep5: alpha=0.3536, lambda=3.736772 
## - Fold03.Rep5: alpha=0.3536, lambda=3.736772 
## + Fold03.Rep5: alpha=0.7569, lambda=0.457474 
## - Fold03.Rep5: alpha=0.7569, lambda=0.457474 
## + Fold03.Rep5: alpha=0.4423, lambda=0.004959 
## - Fold03.Rep5: alpha=0.4423, lambda=0.004959 
## + Fold03.Rep5: alpha=0.4111, lambda=0.885269 
## - Fold03.Rep5: alpha=0.4111, lambda=0.885269 
## + Fold03.Rep5: alpha=0.4419, lambda=0.014470 
## - Fold03.Rep5: alpha=0.4419, lambda=0.014470 
## + Fold03.Rep5: alpha=0.2539, lambda=6.506213 
## - Fold03.Rep5: alpha=0.2539, lambda=6.506213 
## + Fold04.Rep5: alpha=0.7034, lambda=0.215777 
## - Fold04.Rep5: alpha=0.7034, lambda=0.215777 
## + Fold04.Rep5: alpha=0.1303, lambda=2.918438 
## - Fold04.Rep5: alpha=0.1303, lambda=2.918438 
## + Fold04.Rep5: alpha=0.9303, lambda=0.013567 
## - Fold04.Rep5: alpha=0.9303, lambda=0.013567 
## + Fold04.Rep5: alpha=0.9076, lambda=3.206257 
## - Fold04.Rep5: alpha=0.9076, lambda=3.206257 
## + Fold04.Rep5: alpha=0.3536, lambda=3.736772 
## - Fold04.Rep5: alpha=0.3536, lambda=3.736772 
## + Fold04.Rep5: alpha=0.7569, lambda=0.457474 
## - Fold04.Rep5: alpha=0.7569, lambda=0.457474 
## + Fold04.Rep5: alpha=0.4423, lambda=0.004959 
## - Fold04.Rep5: alpha=0.4423, lambda=0.004959 
## + Fold04.Rep5: alpha=0.4111, lambda=0.885269 
## - Fold04.Rep5: alpha=0.4111, lambda=0.885269 
## + Fold04.Rep5: alpha=0.4419, lambda=0.014470 
## - Fold04.Rep5: alpha=0.4419, lambda=0.014470 
## + Fold04.Rep5: alpha=0.2539, lambda=6.506213 
## - Fold04.Rep5: alpha=0.2539, lambda=6.506213 
## + Fold05.Rep5: alpha=0.7034, lambda=0.215777 
## - Fold05.Rep5: alpha=0.7034, lambda=0.215777 
## + Fold05.Rep5: alpha=0.1303, lambda=2.918438 
## - Fold05.Rep5: alpha=0.1303, lambda=2.918438 
## + Fold05.Rep5: alpha=0.9303, lambda=0.013567 
## - Fold05.Rep5: alpha=0.9303, lambda=0.013567 
## + Fold05.Rep5: alpha=0.9076, lambda=3.206257 
## - Fold05.Rep5: alpha=0.9076, lambda=3.206257 
## + Fold05.Rep5: alpha=0.3536, lambda=3.736772 
## - Fold05.Rep5: alpha=0.3536, lambda=3.736772 
## + Fold05.Rep5: alpha=0.7569, lambda=0.457474 
## - Fold05.Rep5: alpha=0.7569, lambda=0.457474 
## + Fold05.Rep5: alpha=0.4423, lambda=0.004959 
## - Fold05.Rep5: alpha=0.4423, lambda=0.004959 
## + Fold05.Rep5: alpha=0.4111, lambda=0.885269 
## - Fold05.Rep5: alpha=0.4111, lambda=0.885269 
## + Fold05.Rep5: alpha=0.4419, lambda=0.014470 
## - Fold05.Rep5: alpha=0.4419, lambda=0.014470 
## + Fold05.Rep5: alpha=0.2539, lambda=6.506213 
## - Fold05.Rep5: alpha=0.2539, lambda=6.506213 
## + Fold06.Rep5: alpha=0.7034, lambda=0.215777 
## - Fold06.Rep5: alpha=0.7034, lambda=0.215777 
## + Fold06.Rep5: alpha=0.1303, lambda=2.918438 
## - Fold06.Rep5: alpha=0.1303, lambda=2.918438 
## + Fold06.Rep5: alpha=0.9303, lambda=0.013567 
## - Fold06.Rep5: alpha=0.9303, lambda=0.013567 
## + Fold06.Rep5: alpha=0.9076, lambda=3.206257 
## - Fold06.Rep5: alpha=0.9076, lambda=3.206257 
## + Fold06.Rep5: alpha=0.3536, lambda=3.736772 
## - Fold06.Rep5: alpha=0.3536, lambda=3.736772 
## + Fold06.Rep5: alpha=0.7569, lambda=0.457474 
## - Fold06.Rep5: alpha=0.7569, lambda=0.457474 
## + Fold06.Rep5: alpha=0.4423, lambda=0.004959 
## - Fold06.Rep5: alpha=0.4423, lambda=0.004959 
## + Fold06.Rep5: alpha=0.4111, lambda=0.885269 
## - Fold06.Rep5: alpha=0.4111, lambda=0.885269 
## + Fold06.Rep5: alpha=0.4419, lambda=0.014470 
## - Fold06.Rep5: alpha=0.4419, lambda=0.014470 
## + Fold06.Rep5: alpha=0.2539, lambda=6.506213 
## - Fold06.Rep5: alpha=0.2539, lambda=6.506213 
## + Fold07.Rep5: alpha=0.7034, lambda=0.215777 
## - Fold07.Rep5: alpha=0.7034, lambda=0.215777 
## + Fold07.Rep5: alpha=0.1303, lambda=2.918438 
## - Fold07.Rep5: alpha=0.1303, lambda=2.918438 
## + Fold07.Rep5: alpha=0.9303, lambda=0.013567 
## - Fold07.Rep5: alpha=0.9303, lambda=0.013567 
## + Fold07.Rep5: alpha=0.9076, lambda=3.206257 
## - Fold07.Rep5: alpha=0.9076, lambda=3.206257 
## + Fold07.Rep5: alpha=0.3536, lambda=3.736772 
## - Fold07.Rep5: alpha=0.3536, lambda=3.736772 
## + Fold07.Rep5: alpha=0.7569, lambda=0.457474 
## - Fold07.Rep5: alpha=0.7569, lambda=0.457474 
## + Fold07.Rep5: alpha=0.4423, lambda=0.004959 
## - Fold07.Rep5: alpha=0.4423, lambda=0.004959 
## + Fold07.Rep5: alpha=0.4111, lambda=0.885269 
## - Fold07.Rep5: alpha=0.4111, lambda=0.885269 
## + Fold07.Rep5: alpha=0.4419, lambda=0.014470 
## - Fold07.Rep5: alpha=0.4419, lambda=0.014470 
## + Fold07.Rep5: alpha=0.2539, lambda=6.506213 
## - Fold07.Rep5: alpha=0.2539, lambda=6.506213 
## + Fold08.Rep5: alpha=0.7034, lambda=0.215777 
## - Fold08.Rep5: alpha=0.7034, lambda=0.215777 
## + Fold08.Rep5: alpha=0.1303, lambda=2.918438 
## - Fold08.Rep5: alpha=0.1303, lambda=2.918438 
## + Fold08.Rep5: alpha=0.9303, lambda=0.013567 
## - Fold08.Rep5: alpha=0.9303, lambda=0.013567 
## + Fold08.Rep5: alpha=0.9076, lambda=3.206257 
## - Fold08.Rep5: alpha=0.9076, lambda=3.206257 
## + Fold08.Rep5: alpha=0.3536, lambda=3.736772 
## - Fold08.Rep5: alpha=0.3536, lambda=3.736772 
## + Fold08.Rep5: alpha=0.7569, lambda=0.457474 
## - Fold08.Rep5: alpha=0.7569, lambda=0.457474 
## + Fold08.Rep5: alpha=0.4423, lambda=0.004959 
## - Fold08.Rep5: alpha=0.4423, lambda=0.004959 
## + Fold08.Rep5: alpha=0.4111, lambda=0.885269 
## - Fold08.Rep5: alpha=0.4111, lambda=0.885269 
## + Fold08.Rep5: alpha=0.4419, lambda=0.014470 
## - Fold08.Rep5: alpha=0.4419, lambda=0.014470 
## + Fold08.Rep5: alpha=0.2539, lambda=6.506213 
## - Fold08.Rep5: alpha=0.2539, lambda=6.506213 
## + Fold09.Rep5: alpha=0.7034, lambda=0.215777 
## - Fold09.Rep5: alpha=0.7034, lambda=0.215777 
## + Fold09.Rep5: alpha=0.1303, lambda=2.918438 
## - Fold09.Rep5: alpha=0.1303, lambda=2.918438 
## + Fold09.Rep5: alpha=0.9303, lambda=0.013567 
## - Fold09.Rep5: alpha=0.9303, lambda=0.013567 
## + Fold09.Rep5: alpha=0.9076, lambda=3.206257 
## - Fold09.Rep5: alpha=0.9076, lambda=3.206257 
## + Fold09.Rep5: alpha=0.3536, lambda=3.736772 
## - Fold09.Rep5: alpha=0.3536, lambda=3.736772 
## + Fold09.Rep5: alpha=0.7569, lambda=0.457474 
## - Fold09.Rep5: alpha=0.7569, lambda=0.457474 
## + Fold09.Rep5: alpha=0.4423, lambda=0.004959 
## - Fold09.Rep5: alpha=0.4423, lambda=0.004959 
## + Fold09.Rep5: alpha=0.4111, lambda=0.885269 
## - Fold09.Rep5: alpha=0.4111, lambda=0.885269 
## + Fold09.Rep5: alpha=0.4419, lambda=0.014470 
## - Fold09.Rep5: alpha=0.4419, lambda=0.014470 
## + Fold09.Rep5: alpha=0.2539, lambda=6.506213 
## - Fold09.Rep5: alpha=0.2539, lambda=6.506213 
## + Fold10.Rep5: alpha=0.7034, lambda=0.215777 
## - Fold10.Rep5: alpha=0.7034, lambda=0.215777 
## + Fold10.Rep5: alpha=0.1303, lambda=2.918438 
## - Fold10.Rep5: alpha=0.1303, lambda=2.918438 
## + Fold10.Rep5: alpha=0.9303, lambda=0.013567 
## - Fold10.Rep5: alpha=0.9303, lambda=0.013567 
## + Fold10.Rep5: alpha=0.9076, lambda=3.206257 
## - Fold10.Rep5: alpha=0.9076, lambda=3.206257 
## + Fold10.Rep5: alpha=0.3536, lambda=3.736772 
## - Fold10.Rep5: alpha=0.3536, lambda=3.736772 
## + Fold10.Rep5: alpha=0.7569, lambda=0.457474 
## - Fold10.Rep5: alpha=0.7569, lambda=0.457474 
## + Fold10.Rep5: alpha=0.4423, lambda=0.004959 
## - Fold10.Rep5: alpha=0.4423, lambda=0.004959 
## + Fold10.Rep5: alpha=0.4111, lambda=0.885269 
## - Fold10.Rep5: alpha=0.4111, lambda=0.885269 
## + Fold10.Rep5: alpha=0.4419, lambda=0.014470 
## - Fold10.Rep5: alpha=0.4419, lambda=0.014470 
## + Fold10.Rep5: alpha=0.2539, lambda=6.506213 
## - Fold10.Rep5: alpha=0.2539, lambda=6.506213

## Warning in nominalTrainWorkflow(x = x, y = y, wts = weights, info = trainInfo, :
## There were missing values in resampled performance measures.

## Aggregating results
## Selecting tuning parameters
## Fitting alpha = 0.442, lambda = 0.00496 on full training set

# Best tuning parameter
elastic_reg$bestTune

##       alpha      lambda
## 6 0.4422599 0.004958862

Metrics for elasticnet

# Make predictions on training set
predictions_train <- predict(elastic_reg, x)
eval_results(y_train, predictions_train, train) 

##        RMSE   Rsquare
## 1 0.6438077 0.3457911

# Make predictions on test set
predictions_test <- predict(elastic_reg, x_test)
eval_results(y_test, predictions_test, test)

##        RMSE   Rsquare
## 1 0.6547278 0.3824665